Have you actually done this to see just how much karma you lose? Lots of bad karma acts have surprisingly low bad karma.
The easiest answer is to not remove the slave collar, though.
It does cost a lot of Karma, since everyone you shoot causes a loss. The sad part is after I cut off the collar, I went a did a few other things, so to re-load a save means a big loss of time. I tried sneaking in with stealthboys, but no luck there either.
I will try the solution suggested above under the spoiler.