My sense is that the reaction of Thomas is not the best place to raise the question of Jesus somehow looking different in the post-resurrection appearances. Thomas had, after all, the testimony of the other ten disciples (or possibly a larger group if "disciples" is not limited to the remnant of the Twelve), and there is the clear expectation that he should not have doubted.
Other Johannine examples
There are other incidents, though. (1) In this same chapter the 'delayed reaction' recognition of Mary Magdelene in John 20:15-16 is recounted, especially:
15b NIV ... Thinking he was the gardener, she said, “Sir, if you have carried him away, tell me where you have put him, ...”
(2) Similarly, the prior visit of Jesus to the disciples (without Thomas) in John 20:20 depicts a positive reaction, with the implication that this comes only after signs of affirming identity:
20 After he said this, he showed them his hands and side. The disciples were overjoyed when they saw the Lord. [ἐχάρησαν οὖν οἱ μαθηταὶ ἰδόντες τὸν κύριον]
The little particle οὖν = oun can signal result ("therefore") or simply consequence ("then/when") and also suggests a "delayed reaction" in the appearance of Jesus to the disciples in Thomas's absence.
(3) A third possible example comes in John 21:4-7 when in the grey light of dawn Jesus gives instructions about fishing, and there again seems to be a delay in recognition:
7 Then [οὖν] the disciple whom Jesus loved said to Peter, “It is the Lord!” As soon as Simon Peter heard him say, “It is the Lord,” he wrapped his outer garment around him....
Here, however, the narrative setting of dawn light and distance might be enough reason to obscure the identity of the one calling from the shore.
Other Gospel parallels?
As an earlier answer notes, there might be a temptation to liken these incidents in John to the Emmaus road encounter of Cleopas and friend with Jesus, post-resurrection. There, however, it seems a different dynamic is at work to explain their lack of recognition (Luke 24:16):
16 but they were kept from recognizing him.
with the NIV here quite mild in representing ἐκρατοῦντο τοῦ μὴ ἐπιγνῶναι αὐτόν = "constrained not to recognize him". In the synoptics, perhaps a more closely related incident to those in John is the doubting noted in Matthew 28:17 (on which see an earlier Q&A, and other related ones linked there).
Beyond the Gospels
It remains, of course, speculative to link the Johannine incidents of failure to recognize the post-resurrection Jesus with the result of the physical abuse he suffered in the course of his execution. There is also Paul's teaching on the resurrection body in 1 Corinthians 15:35-49 (+ cf. Philippians 3:21) which implies that resurrection bodies have a different character than mortal bodies, especially vv. 42-44a:
42 So will it be with the resurrection of the dead. The body that is sown is perishable, it is raised imperishable; 43 it is sown in dishonor, it is raised in glory; it is sown in weakness, it is raised in power; 44 it is sown a natural body, it is raised a spiritual body. ...
In the final analysis, then, one cannot be sure that Jesus' post-resurrection "recognizability" is entirely down to the ravages experienced in the passion, as the wider NT witness suggests that the resurrection body has a distinct character from the mortal body in any case.