For my current playthrough, I'm collecting all the skill books. I already did the
Galaxy News Radio quest, but at the time I hadn't thought of the weapons
cache. I already obtained the Guns and Bullets skill book in there buy using
frag grenades, but I was wondering... Is there some other way to obtain the
key so I can go in and get the rest? I'm pretty sure there isn't - but I thought
it couldn't hurt to ask anyway. Thanks in advance!

im afraid not.

the only way in is with the key, and the only way to get the key is a successful speech check during the quest

That's too bad. Oh well, at least I managed to still get the skill book inside. Thanks anyway!