Looking for non-dairy alternative to yogurt in chicken tikka masala

Coconut yogurt. I've been making my own both on my counter and in my Instant Pot. You just need to get ahold of live probiotics. I got mine from Amazon, but I'm sure you can find them locally.

There is now (but I haven't tried it yet) such a thing as coconut-based yogurt. Would that work for you?

Raw cashews blended with some water

Coconut milk? You may want to add less because a tikka masala sauce is supposed to have some heft to it....but I think it would give it a bit of lovely South Indian flavor.