I'm still right near the game start, and am moving towards Drassan. One of my mercs was injured in a random encounter. When I resume travel, she pops up saying something and the game crashes. I've tried assigning new waypoints, destinations, etc, but the game keeps on crashing as soon as I unpause it.

It might be she's too injured or too tired to travel.
Find a good spot in the sector to take cover.
Rest and heal your wounded soldier there.

Yes. By "crashing", of course, I mean my game is crashing. As in, it's crashing back to my desktop, and I have to restart the application.
So while I'd love to park the hysterical little queen in a nice shady spot with some unicorns and magic elderflower wine to restore her spirits, I can't. Because the game crashes.

Don't travel but stay in the sector.
Go down from tactical screen to the sector and place your mercs at a save place, like inside a building if available.
Wait till the injured merc is strong enough or leave her there and have the rest move on.
Save regular and always before traveling or entering a hostile sector.

For some reason, the tactical/map swap button was inactive. I ended up restoring an earlier game and starting over from there.