I'm a cellist and I have been parent coach for Suzuki viola. I don't have specific experience with this, but will use my imagination.
Let's renumber the fingers. What used to be "2" will now be "1" and so on. Your student will be working with fingers 1, 2 and 3. Think of a beginning student who doesn't use the fourth finger yet.
Now, let's think about how to play a scale that doesn't use open strings, for example A flat major. When the violinist has four fingers available, it is possible to play the whole thing in one position, without shifting. That's not going to work now. Here are some possible approaches ("change" will mean "change strings"):
A: 1 - 1 2 3 change 1 - 1 2 3
B: 1 2 - 2 3 change 1 2 - 2 3
C: 1 2 3 - 3 change 1 2 3 - 3
D: Always play six notes on one string before shifting to a lower position.
I think I like B the best of the first three.
C has the advantage that it's similar to a pretty common fingering I've seen for three-octave scales, where one repeats 4 at the top of the scale.
The challenge with D will be to maintain a solid tone in the higher register of each string.
I think you could simulate what your student will experience by putting a bulky bandaid on your left index finger, so as to avoid using it. This will make it easier for you to try things out yourself before you suggest them to your student.
While your student is getting the hang of this new way of playing, I think he should avoid doing anything on the G string. Reason: the center of gravity is going to be more towards the new third finger than before, and this will require swinging the elbow around more than normal. Playing on the G string already requires one to bring the elbow around, which is unnatural, so let's not overdo it at the beginning.
I think the thing that will be the hardest to adjust (and sometimes not possible to play, as written) will be certain chords (triple stops). I would not hesitate to do a little rewriting of pieces, such as Bach, that have some triple stops that aren't working. For example, you could omit the middle note, and play the lower note as a grace note before the main note. When saxophonists play Bach cello suites, this is how they interpret triple and quadruple stops.
In terms of inspiration, even though the anatomy and mechanics are different, it might be inspiring to take a look at Jessica Cox, born with no arms. She explained in a short documentary (2 minutes in) that for her, a turning point was to see another woman with no arms caring for her baby, picking up the baby, changing the baby's diaper. Cox is very upbeat.
You and your student may also want to think about a prosthetic.
I haven't found a video of Cox playing piano with the audio, but I did find a short one that shows her playing, visually. It also shows her doing a variety of daily living activities, such as brushing her hair, eating dinner, typing on her computer. This is a good video for you, I think, because she explains how helpful her parents' can-do attitude was -- right from birth.
I think the other key thing for Cox's development, in terms of self-esteem and creative problem solving, must have been watching the mother caring for her baby. Cox has made a point of making herself available to children with her disability, realizing, I think, how important it is to make that connection.
I myself have seen how helpful that connection with others with the same disability can be. My son has Tourette Syndrome and OCD. He has found the following hugely helpful:
watch videos of Tim Howard (famous soccer goalie with Tourette and OCD), both playing soccer and being interviewed about his disability; and read Howard's autobiography
meet other young people with Tourette Syndrome at conferences and family retreats