Installing LAME first then Audacity really isn't as big a deal as you're making out - you'd think someone had asked you to sacrifice a goat before you can use the software
I use Audacity for the exact process you describe and it's perfect for such a trifling little audio editing job - highlight track, ctrl-c, ctrl-n, ctrl-v and the cut out bit is there in a fresh new window waiting for you to further crop, fade in/out, normalise etc. before exporting as MP3. Bish bash bosh.