Yes, calling one's self "expat" instead of "immigrant" sounds exactly like what someone who goes elsewhere to avoid taxes and draft service, while driving up the local housing market and enjoying cheap labor, would do.
Again, if strength is important, then use strength as the draft criteria, not gender.
And, you do realize that the vast majority of the military aren't combat troops, right? Drone operator duty doesn't require high grip strength. Logistics managers don't require high general strength.
Is your sexism blinding you to the female soldiers who served in the Gulf War, Iraq, and Afghanistan? What do you think they were doing if not being soldiers?
A small set of counter examples do not invalidate broad generalizations. And if my state wants to commit economic suicide and there is no way for me to stop it I feel no need to join it.