Possibly, if you're not careful in the making of it. But if you are, there are only the wood fibers, which can't be traced to an already burned and buried weapon.
And that ice knife would carry similar microscopic traces of you if you're not careful. So, unless you live in the tundra or it's the dead of a hard winter, the wood knife is still a better choice...
Sure there is similar microbes to be traced in water but it would be harder to trace especially if made with tap water and the fact is not easily collected or seen off of your person. Lol
Either way you're going to get caught in this day and age, unless you wrap yourself and your prep room in plastic before beginning. And there's still evidence to burn afterwards.