Here are even more reflections on the non-combat skills DF templates bring to the table. These are based on my experiences in my game; your own experience may vary!
Possibly the most useful non-combat skill you bring to the table is Exorcism. With it you can clear cursed areas, banish evil spirits, and otherwise purge areas of evil. It's not fast or easy, but it's a potentially mission-critical skill. Without it, all you did was kill some temple guards or demons and steal some loot - the root of the evil is still there. With Exorcism you have a chance to finish the job.
Not healing? No, that's basically a combat ability. That you also have post-combat slower healing skills (First Aid, Surgery) and optionally abilities (Healing) is extremely helpful, but it's basically a "recover from combat" ability. Most of your skills support healing or Exorcism.
Besides those, it's really a question of your skill picks. Panhandling to beg for money, Savoir-Faire (High Society) for dealing with bigwig quest givers, Research and Writing for finding things out before your delve or writing up what happened afterward.
Excellent outdoors, the Druid really doesn't need a lot of text to explain its utility outside.
Inside, you're always limited by penalties to spells and skills focused on trees and plants and animals. The non-combat skills you do have mostly feed into the outdoors or the combat skills you have.
That said, even in a dungeon druids have solid Per (base 14) and FP (base 13), so you're good at spotting things and usefully sturdy as well. You also have access to Poisons and a weapons load that really pushes for their use.
Outdoors, you're golden. Indoors, try to leverage your Background skills as much as you can and be a useful spellcaster within the confines of your penalties.
Perception. Outdoor abilities. You are great at both of those. Your Per 14 is equal to that of the druid, but you're a bit faster and more oriented towards combat in case your scouting doesn't quite work out so well.
Beyond that, Tracking will help you find the lair of foes, especially if you are looking for the origin of wandering monsters or roving patrols. Cartography could help, but you're going to want two hands for a bow, not one for a shield with a lectern mount and one for a pen.
Out of your Background Skills, a few are especially useful in dungeons. Prospecting will help with all of that tunnel delving and spotting potential natural sources of treasure (ore), at least in my games. Seamanship will help in non-dungeon trips but Boating comes up more often than you'd like in megadungeons. Knot-Tying is useful for taking prisoners, and Swimming has saved a scout in my games.
Overall, your focus is ranged combat but you make a pretty good point man even in a group with a druid, and a good backup for a stealth-focused thief.