Council of Trent and rubrics
A word search of the English version of the Proceedings of the Council of Trent did not, when the term relic shows up, address that detail. There may have been other supplemental guidance offered under various papal bulls or decrees, but in the Council of Trent's issued declarations that detail is not found.
The prose declarations made on pages 233-237 address the veneration of saints and various prohibitions in unverified new relics, or unseemly depictions of saints, but not a rubric on how a relic is to be packaged. The Council did rule that relics required review and authentication by the episcopal authority in order to be permitted for public veneration.
While another council may have included such rubrics on reliquaries, the Council of Trent appears not to have done so.
From the Catholic Encyclopedia entry on reliquaries:
Lastly it will be sufficient to point out that relics have at all
times been kept in simple caskets or boxes, varying indefinitely in
size, material, and ornamentation. In more modern times these are
invariably secured by a seal, and the contents indicated in a formal
episcopal act of authentication, without which it is not Lawful to
expose the relics for public veneration. The silver box containing the
head of St. Agnes, recently brought to light in the treasury of the
Sancta Sanctorum, still preserved the seal of some cardinal deacon
affixed to it apparently at the end of the thirteenth century.
Of the various documents available regarding relics and reliquaries, the consistent requirement is that any relic (to be a relic as opposed to something else) must be accompanied by an episcopal documentation of authenticity. While that isn't a matter of "packaging" or handling, it looks like a hard requirement.
The Collectio Rerum Liturgicarum of Rev. Joseph Wuest, C.SS.R., Latin - 1889
Matters Liturgical by Rev. Thomas Mullaney, C.SS.R., English translation - 1925
Authenticity of Relics. Only those relics can be honored with a public cult in churches, even though exempt, which are certified as
genuine in an authentic document of a Cardinal, a local Ordinary, or
an ecclesiastic to whom the faculty of authenticating relics has been
granted by apostolic indult (c. 1283, 1).
b) Without a special mandate a Vicar General cannot authenticate a
relic, even if there is merely question of authenticating a relic
taken from a relic already duly authenticated, or of issuing a new
certificate of authenticity, or of placing a seal upon an
authenticated relic (c. 1283, 2; CODE COMM.: JULY 17, 1933).
c) Local Ordinaries shall prudently withdraw from public veneration
any relic which they know is certainly not authentic (c. 1284).
d) If the documents of their authenticity have been lost as a result
of civil disturbance or some other mishap, sacred relics shall not be
exposed for public veneration without the express approval of the
local Ordinary; this approval cannot be given by the Vicar General
without a special mandate (c. 1285, 1).
e) What is stated above (d), does not apply to ancient relics. These
shall be venerated in the same way as heretofore, unless for reasons
that are certain it is evident that the relics are false or
supposititious (c. 1285,2).
You will find on pages 18 and 19 of this document a description of "The Authentic" and some of the details of authentication to include the affixing of seals and the use of crossed threads.
Underneath the back cover of the relic locket there is a seal of red
wax. The relic secured in place in the locket by threads that cross
over it. The threads are inserted through the walls of the locket on
the opposing sides and it is sealed shut with a wax seal bearing the
insignia of issuing religious authority and there order's initials.
This seal and its locking procedure (threads and seal) should never be
broken or cut. It protects the integrity and validity of the
Source/caveat: Public Veneration and Exhibit Manual; 2000; Thomas J Serafin; (ICHRusa). That makes this a contemporary source.