You're best bet is to make a template of the area you plan to attach the partial to.
Then you can place that on the underside of the lace base, draw around it with a make-up pencil and then cut it with your blade.

You really don't have to be that exact or precise, just careful.
Running a sharp blade on the underside of the lace will cut the lace but avoid the hairs knotted to it, but its inevitable you'll lose a few hairs along the way.

As for the Ultrahold glue, this can be notoriously difficult to work with and many people prefer to use an artist's brush to apply it.
Its stringy and messy.
Its also difficult to clear up from & clean off the skin & base.
The normal alcohol based removers have very little effect on dissolving the glue and you really need something acetone based like nail varnish remover.

Its all a bit harsh on the system.
You might want to consider one of the white glues like NEX GEN, Ghostbond XL or ORWG (oil resistant white glue).

Good luck!

http://youtu.be/jw3_djdio9c