I would like to add to the answers already posted a few observations about the theological lexical register of the Biblical writers that may bear on the OP's question.
Is there any lexical support for [sin as rebellion] (either through a sub-sense of those words, or through other words)?
Yes. This is true both in the OT and the NT. The NT understanding of sin is the development of a Hebrew concept, and the vocabulary follows suit. Thus, although, as pointed out by the OP, the Greek ἁμαρτία (and a slurry of cognates) in Ancient Greek denoted "missing the mark", they are frequently used in the LXX to represent the particular Jewish notion of sin.1 In the NT these words are never used without these moral connotations (NIDTTE). This Hebrew background is therefore of primary importance in understanding the meaning of the NT authors.
In Hebrew, there are indeed other words conveying the notion of sin. The OP mentions חטא (ḥṭʾ), which can be used outside the moral realm to mean "to be mistaken" or "to miss". (See, for instance, Judg 20:16, of archers who could sling stones and not "miss" (ḥṭʾ).) The term is also used to express interpersonal ethical lapses (e.g. 2 Kings 18:14). The most common use in Biblical Hebrew, however, is in the theological sphere, where it denotes failure in one's obligations toward God, particularly in the legal and cultic domain. This is the most common word used for sin, used ~595 times. It contains no a priori notion of rebellion.
However, there are many other words that express related concepts of human evil sometimes translated "sin".2 The most relevant here is the term פשע (pšʿ) (~145 times). Unlike ḥṭʾ which can refer to a mere mistake (primarily cultic inadvertences), pšʿ essentially means "rebel", also sometimes translated "revolt" or "transgress".3 In interpersonal relationships, it means "willful violations by an inferior against a superior" (Luc; see, e.g., Gen 31:36, Prov 28:24). In man's relationship with God, this sense is preserved:
In biblical theology, the term refers to an open and brazen defiance of God by humans.
This, then, is the word that denotes the aspect of sin that comes closest to the notion of rebellion. Not surprisingly, it is a favorite of the (latter) prophets, where the role of Israel's pšʿ in their broken relationship with Yahweh is relentlessly rehearsed.
These prophets...make repeated use of pšʿ because their ministries devote significant attention to Israel’s past or present covenant treachery. They indict Israel for disrupting their covenant relationship with Yahweh. Isaiah begins his prophecy by depicting Yahweh’s relationship with Israel in terms of a father-son relationship. Israel, although a recipient of Yahweh’s abundant, tender care, has rebelled against her father (suzerain) (Isa 1:2) and faces severe judgment (1:28) (Carpenter).
A few (of many available) examples that well illustrate this theme:
Woe to them, for they have strayed (or fled) from me!
Destruction to them, for they have rebelled (pšʿ) against me!
because they have transgressed (lit. passed by) my covenant
and rebelled (pšʿ) against my law.
Children have I reared and brought up,
but they have rebelled (pšʿ) against me.
Rebellion is thus central to pšʿ.
The OP further asks:
Are there any passages which define or equate sin and rebellion?
Other answers have given many relevant conceptual parallels, the connection with Genesis 3 (which uses neither of these terms!4 ) being the strongest in my mind. This is summarized by Bloesch:
It should be acknowledged that sin entails both privation and positive rebellion, but the latter is prior to the former. "The origin of pride," says the prophet, "is to forsake the Lord, man's heart revolting against his Maker" (Ecclesiasticus 10:12 NEB).
To expand on this idea with a bit of lexical precision, I will just point out that, although they certainly emphasize different aspects of sin, the Biblical writers recognized close connections between ḥṭʾ, pšʿ, and other terms in this semantic domain (most prominently ʿwn). Isaiah states this directly in terms of their common end (1:28):
But rebels (pšʿ) and sinners (ḥṭʾ) shall be broken together,
and those who forsake the LORD shall be consumed.
The Psalms include repeated rehearsals of synonymous parallelism using these two terms. This is often formulated in terms of Yahweh's grace, which, as with his punishment, applies "together" to every brand of evil entertained among men:
I acknowledged my sin (ḥṭʾ) to you,
and I did not cover my iniquity (ʿwn);
I said, “I will confess my transgressions (pšʿ) to the LORD,”
and you forgave the iniquity (ʿwn) of my sin (ḥṭʾ). (Psalm 32:5)
All English is ESV unless otherwise stated.
1. There are, of course, many other terms. See, Trench, "Synonyms of the New Testament", p. 239ff, for an extensive discussion. As pointed out by Silva (NIDTTE) and undoubtedly many others with modern linguistic sensitivities, the etymological distinctions drawn out there are not necessarily meaningful with respect to NT usage. Silva, regarding the dominance of ἁμαρτία + cognates:
[U]sing the language of semantic hierarchy, ἁμαρτία may be viewed, with some qualifications, as the superordinate of the other nouns, which are its hyponyms... But more important, within a theological framework, ἁμαρτία becomes for the NT writers the key term to express the fallen human condition.
2. Excerpted from NIDOTTE's index of semantic fields: אָוֶן (mischief, iniquity, deception, H224); חָטָא (sin, commit a sin, purify, H2627...); עָוָה (do wrong, pervert, H6390...); עָוַל (act wrongly, H6401...); פָּשַׁע (rebel, violate, transgress, H7321...)
3. Like ḥṭʾ, pšʿ has both noun and verb forms that are both very common. Both also can be used as participles: "sinner", "rebel", etc. I have represented all of these with the root consonants here.
4. In fact, none of the common words for "sin" is used in the Gen 1-11 saga that is so formative for the Hebrew notion of sin, with the single exception of Gen 4:7 (as if we needed another source of obscurity in that verse).
"ἁμαρτάνω". New International Dictionary of New Testament Theology and Exegesis. Ed. Moises Silva. Zondervan, 2014.
Donald G. Bloesch. Essentials of Evangelical Theology. Prince Press, 1978; 1:93.
Eugene Carpenter, Michael Grisanti. "פשע", New International Dictionary of Old Testament Theology and Exegesis. Ed. Willem A. Wangemeren. Zondervan, 1992; 3:705.
Robin C. Cover. "Sin", Anchor Yale Bible Dictionary, Ed. David Noel Freedman. YUP, 1992.
Alex Luc. "חטא", New International Dictionary of Old Testament Theology and Exegesis. Ed. Willem A. Wangemeren. Zondervan, 1992; 2:90ff.