And that's exactly what they'll do- use Fate. They'll also tend to be more timid and try to approach combats more tactically to avoid getting shot. In a given session, I tend to have 2-3 fights. This is mainly because combat tends to take forever and a day to resolve and the players wouldn't be able to do anything else.
The only real problem having no Apothecary that I've seen, or a small group, is one of balance for the GM. Creating a not-to-tough-but-tough-enough challenge for PCs is harder when they might be able to heal 1 wound, or they might be able to heal 10, is one more variable in go big or go home damage system of DW.
In my experience, until you're an expert at blancing (in which case I envy you), you may need to fudge some rolls with a smaller group to keep from wiping them out. With a Tech, Dev, and Assault you've got a pretty good mix I think; heavy range, heavy close combat, and the 'everything else' guy. Give your players plenty of opportunity to use tactics to outsmart their enemies and reward them for that, and they can escape combat with only a few scars, saving their wounds for your elites and masters.