So, because I fancy having nice little outfits, I wanted the Hammerfell garb/Scimitar weapon.

I'm siding with the Alik'r in finding the redguard woman, will me sneaking and killing one of the random warriors affect me in a bad way?

I don't know the answer to your particular question, but I know there is at least one peaceful way of getting a copy of those items.

There is an overturned boat west of Dawnstar with a schmitar, and some of the garb. There is a lighthouse to the east of Dawnstar (with a quest and a few rewards) with a full set of garb.

You can buy the outfit from that stuck up [censored] in solitude,

I did it once, and nothing bad happened. The woman was muttering "I'm going to find whoever did this."

Make a save point and try it. Nothing to lose.

If you kill them in front of a witness, I think it's considered a crime. But the redguard woman does not count as a witness, in my experience.

Kill that daedra in the Midden

In addition to the other sources people have mentioned: Kematu and his band will be in Smuggler's Den for a little while after you complete the quest in his favor. I'm pretty sure they'll aggro you so you won't have to attack first.

Radient Raiment in Solitude sells the clothing