Shipping would be a major hurdle for CCA. Anyone that has a serious look at their relative size compared to typical Cruise missiles would understand that crating operations would have to be made with much more voluminous items, restraining the number that can be airlifted rapidly to a theater of operations.
Then there is the possibility to let them fly to their destination like any fighters are deployed. Sadly, the economy of scale for affordable systems, including how their engines are selected and built for low flight hours, given the need to be attritable, will restrict the ability of self-deployment by sending them on a long flight to their destination. That would even be a rarity (unless a special deployment engine, used in that case in-lieu of the normal one, can be sourced with longer TBO and ease of replacement).
So the question is not even STOL or not STOL. It's would certainly be all about having them prepositionned/assembled in theatre until the solution is found. Hence, it would be primarily a matter of affordability.
That's why we can guess this aspect is the strongest factor in their selection, beyond VLO, beyond having a WB.