Do i have to be on a quest in order to get the dragon shout on the wall in a cave? Or can i just roam the cave without being on a quest and still get the dragon shout?

you don't have to be on a quest...

as long as you can get close enough to the word-wall, you will unlock its word of power

A few shouts are in quest locked caves or locations, but most are not. And, a number of shouts are in caves or places that are part of a quest, but that should not stop you from getting the shout. Just be careful of any unique named loot you might come across, it might be quest related.

Which is a terrible thing. My Dragonborn can't be at his full potential. He'd have to join the College and TG to get a few extra shouts.

Are you on PC? There may be a solution if you are...

PS3.

Ah.

Well, I was mistaken anyway, the mod in question was taken down.

If they really had to quest lock shouts, they should have at least made the shouts pertinent to the questline it's locked in. Why is disarm locked in a TG quest? Makes no sense.