A lot of stuff can destroy walls. A pickaxe is indeed the dedicated early-game tool for that. Explosives, as you've discovered.
Due to damage scaling to stats, a bunch of the bigger melee weapons can be used to dig as well once you have a jacked agent. The picture from before had a mid-game-ish agent using a plain axe to dig through walls. A bardiche is even better.
It's kinda silly in that that the same soldier from the last picture can do this (even with a regular axe, though it takes a few tries to knock down one wall; the giant axe usually only needs one swing), removing any need for endgame laser cutters and fusion torches. But Solarius likes his melee.