No trinket gunner. Update January 3, 2015: deciding on UV'S.

Is there a build that gives you damage equivalent to some sword without trinkets?

I'm not sure what you mean. Charging Blitz Needle with damage+6, CTR+6, ASI+6 is crazily powerful. Is it "equivalent to some sword"?

You can definitely exceed the power of swords with guns nowadays. You could before as well, but it was quite limited to Alchemers and Blitz Needle (Pepperbox as well?). Now there's two autoguns, two alchemers (counting ones with the most power), and three Magnuses which are essentially Brandishes in terms of charges.
As for what you bring along with them, you'll want Chaos or Black Kat Set but if you're doing the latter, you'll want trinkets, UVs, or perks to boost CTR. Since you did ask about no trinkets, though, Chaos is better. I'm assuming you're not interested in UVs either. A sprite perk might be relevant, though? Either way, with heat+Chaos you get CTR Max and DI Very High on all weapons and that's silly powerful. Add swiftstrike and a sprite perk and you can get up to CTR Max, DI Max, and ASI High.

what do you mean by heat+chaos? Thinking back on my original post, maybe i'll punch some of my guns.

He means heat level 10, which gives you CTR+2. Combined with the CTR+4 from full Chaos, you get CTR+6.

If you're looking to build hyper-specialized equipment, then monster-specific damage bonuses are valuable. For example, if you want a set specifically for slimes, then slime UVs, Deadly Virulisk, and stuff like that is valuable.
However, most players, including me, do not want such specialized equipment. Collecting it is too expensive and equipping it takes too much hassle. Also, such equipment never gives damage bonus against Vanaduke or other knights in PvP. To get that, you want blanket damage bonuses against all enemies --- the kind you get from Skolver, Shadowsun, Chaos, etc.
For these reasons, I regard damage UVs on weapons to be worthless. The only weapon UVs worth thinking about are ASI and CTR. Which one you focus on depends on the weapon, whether you wear Chaos, etc.
Probably you know all of this already. I mention it only because you now seem to be seeking advice on UVs. There's nothing more to say without knowing your weapons and armor.

Armor:
- Chaos [lv. 5]
- Swiftstrike [lv. 3]
Weapons:
- Callahan [lv. 7]
- Mega tundras [lv. 9]
- Argent peacemaker [lv.4]
- Black chain [lv. 7]
Sprite lv. 83, Trueshot 1

Get an alchemer instead of an Argent Peacemaker. Trying to use only an antigua for a few runs straight will make your trigger finger fall off in protest. Also, Alchemers are amazing if you're good with them.

ok, I take it double/single switching would be a viable strategy for optimal output with those weapons since, to my understanding, are two shot clips, yeah?

That is correct. Good use of ricochets can probably in some cases be more important, though. No reason to not do both, however.

I agree with replacing Argent with an alchemer. Go for ASI UVs on your guns. Using your sprite perk for handgun damage is good, but consider also using it for movement speed increase.
Chaos
Black Kat
Those are the strongest, I've never used any gun buffing stuff but a seerus mask so there's my guess at it