Would it be possible to make an actor do a throw motion as if it were throwing a grenade? I have a throwing gun but I'd prefer it doesn't look like my thrown weapon randomly appears in front of me.

nope

we have next-to-nothing we can do with limbs, and that's unfortunately unlikely to change in future builds

Do it reverse. Have a TDExplosive that adds itself back to the actor.

But I don't want it to ask how hard I want to throw it...

Then have it set it's own velocity after being thrown, so that just clicking once works.

I don't wan't it to show the dotted line though, and I've set the thrown weapon to be somewhat slow, but automatic. That wouldn't work with the grenade idea. I guess I'm out of luck...

you could make it give your actor an item with offsets that make your actors hands move in front of them that destroys itself a frame after appearing.

That's a great idea! Thank you!