I’ve heard good things about using ice hockey stick tape for this purpose from a few people on Discord. Apparently, it’s as thin as band-aid fabric. This is the one I ordered and that I plan on trying out:
https://www.amazon.co.uk/dp/B00HYEGK7W?th=1
You can also use small, 0.5 mm thick silicone pads. We talked about that in this thread.