According to Catholicism, how did Jesus go in secret (disguise) to the Feast of Tabernacles?
8 You go up to this feast. I am not yet going up to this feast, for My time has not yet fully come.” 9 When He had said these things to them, He remained in Galilee.
10 But when His brothers had gone up, then He also went up to the feast, not openly, but as it were in secret.- John 7:8-10
It would seem plausible that the term secret in this passage of Scripture simply means some more or less by himself or privately or on his own. Sorry no disguise was needed or used by Our Lord.
Let the Church Fathers speak for the Church!
Finally, after He had said these words, When His brethren had gone up; the Gospel declares it, attend, read what you have objected to me; see if the passage itself do not solve the difficulty, see if I have taken from anywhere else what to say. This then the Lord was waiting for, that they should go up first, that they might not announce beforehand that He was coming, When His brethren had gone up, then went He also up to the feast day, not openly, but as it were in secret. What is, as it were in secret? He acts there as if in secret. What is, as it were in secret? Because neither was this really in secret. For He did not really make an effort to be concealed, who had it in His Own power when He would be taken. But in that concealment, as I have said, He gave His weak disciples, who had not the power to prevent being taken when they would not, an example of being on their guard against the snares of enemies. For He went up afterwards even openly, and taught them in the temple; and some said, ' Lo, this is He; lo, He is teaching.' Certainly our rulers said that they wished to apprehend Him: 'Lo, He speaks openly, and no one lays hands on Him.' - Sermon 83 of St.Augustine on the New Testament
St. John Chrysostom adds this to your question:
For, says the Evangelist, Jesus, when He had said these words, abode in Galilee; but when His brethren had gone up, then went He up also unto the feast, not openly, but as it were in secret. The expression, when His brethren had gone up, is that of one showing that He chose not to go up with them. On which account He abode where He was, and manifested not Himself, although they in a manner urged Him to do so. But why did He, who ever spoke openly, do so now as it were in secret? The writer says not secretly, but, as it were in secret. For thus, as I have said, He seemed to be instructing us how to manage matters. And, apart from this, it was not the same to come among them when heated and restive, as to do so afterwards when the feast was ended. - Homily 49 of St. John Chrysostom on the Gospel of John