Maybe rethink the gun. They have these things that use rapidly (but, crucially, not instantly) expanding liquid nitrogen to propel sensitive payloads real fast. I saw a study about using them to throw bombs on mountains for avalanche prevention. Maybe a small one could work to ice someone (hah).

Also, there is an ice-adjacent material that could make the bullet named pykrete which is more durable than pure ice (Mythbusters made a boat made out of it one time). That defeats the purpose of an ice bullet somewhat, but who knows, sawdust might just confuse the forensics.

I spent way too long thinking about this.