Wood has traditionally been used for knife handles without stabilization. Stabilization only widens the variety of woods that can be used. Theoretically one can make balsa wood hard enough for use as knife handles with the addition of enough stabilizing resin.
Traditional woods such as cocobolo, ebony and lignum vitae don't really benefit from stabilization. Desert ironwood is another wood that doesn't need the process.
I have had people who stabilize wood tell me that cocobolo will ruin the resin they use because of the oils in it. Lignum vitae had so much oil in it that it is still used as bushing blocks for the propeller shafts in ships and for bushings in grandfather clocks. It won't take a finish when used as knife handles. Just sand it and polish it with fine Jewlers rouge because no finish will stick to that oil.
I have seen knives advertised as having stabilized cocobolo handles, but I question the effectiveness of it. The process is billed, in part, on the amount of resin the piece of wood absorbs. If the weight of the piece of wood only increases a few percentage points one must question the effectiveness of the process.
I would not allow the fact that wood is not stabilized keep me from using it. As long as the wood is good and hard I wouldn't let it bother me.