1. Unchambered? I'd think about a revolver then, as you're basically going old west cowboy style. This used to be a time honored tradition as (supposedly) cowboys etc. would put their hammer on an empty chamber in the cylinder as they didn't trust it enough. Put the hammer on an empty chamber. If it helps your mind then cool. You still have five rounds and it won't affect your trigger pull or anything. I'd recommend this as your best option if you already liked revolvers. Jframes are nice and tiny.
2. Alternatively, get yourself a pistol with a nice manual safety and a good holster. As you mentioned LCP I'm thinking you're looking at small pistols in the .380 range. I'd recommend a Sig 238 or Colt Mustang. Both have good manual safeties. If you're uncomfortable carry it for a week cocked and locked, but have the chamber empty. I too had this concern for quite a while. I did this for a week and was comfortable enough to go full cocked and locked by day 3.
Having said all that the wife is still not comfortable as much as I have bugged her about it. She carries without one in the chamber and we practice a fast draw and simultaneous cocking. I'm not happy but its that or nothing so I'll take that.
EDIT: Here's a youtube of the Israeli Draw method. It may be helpful if you keep the route of an automatic with an empty chamber.