Our every interaction is like looking at my younger self but I still find that I do not know what the “right” thing to do is!

Our every interaction is like looking at my younger self but I still find that I do not know what the “right” thing to do is! For context: I am 16 and my school makes me volunteer every week. My volunteering involves listening to children read or helping them to discuss and improve their essays. I am naturally very shy and I stammer so I find it to be quite difficult to interact with children because I fear them laughing at me but it is compulsory so I go regardless. Initially, every week, I would end up with a different child (with occasional repeats); now I often have the same child. This boy reminds me very much of myself when I was his age. He is quite intelligent and seems to have a great interest in most of the subjects I end up discussing with him. His main problem is that he lacks confidence. He is very shy. Furthermore, when he reads aloud (though not when speaking in the regular way) he stammers. He has repetitions and blocks. It seems to me that it does frustrate him and he tends to be thrown off by the first instance which increases them after that point. Hearing him read aloud was actually the very first time I had heard any other person stammer in my entire life. I had never experienced being the one to hear somebody else do it. I must admit that it made me feel slightly uncomfortable and self-conscious, just as much as it made me feel some type of relief and sympathy. Never has he directly reacted to my stammering and, likewise, I have never made any comment in his, nor do I include any explicit reference to it when I write my reports in his reading diary. It is like this big unspoken shared thing that seems to permeate every interaction. I do not know if he chooses to be partnered with me each week or if we were paired together for this reason but, outside of lessons, he approaches me on the grounds not infrequently and will make small talk with me. He treats me very respectfully (he calls me sir lol) and he does seem excited to speak with me and doesn’t have the same shyness that I observe in him that I did when we first met. I secretly find it endearing that he clearly likes speaking with me. I find myself in two minds over this. For one thing, I do still feel quite self-conscious of my stammering and I do wonder whether it is bad for him to listen to me talking. Even if it makes him feel better in the short term, what if I am hindering his ability to read aloud because I don’t address that he stammers? On the other hand, maybe it is good for him to realise that he isn’t the only person who talks like this? Maybe being more confident is enough? Should I be doing something else or is it okay to not want to bring it up? Is it selfish that I won’t mention his stammering just because I would hate to talk about mine (which is much more severe than his?) - all because I feel like a self-conscious hypocrite? I think it would probably be better for his speech to work with somebody else but I had also been told by the teacher who organises the pairings that he is more engaged now than before so maybe it is good for him on some other level to be paired with me? To be honest, as many times as it makes me feel good, it makes me feel bad about myself. I don’t know whether I should ask to not work with him or to question why we are together or even if I should change my approach? Please can I have some advice: If you were me, what would you do? If you were the boy, what would you want me to do?