I solved my problem and thought I'd pass along my solution.
The recording screen isn't completely skinnable and when I looked through the source code to make a change I decided that was going to be way too hard. I ended up choosing a theme and modifying it so that the recording status icon would be displayed while I was recording & no icon would be displayed in that spot when I wasn't recording. I also removed three other things from the status bar. That's enough for me.
Details:
I chose the Pony Theme for my Clip V2. I renamed all four files (Pony.cfg, Pony.wps, Pony.sbs, & Pony.fms) to be called BasicRecPony.cfg, BasicRecPony.wps, BasicRecPony.sbs, and BasicRecPony.fms. I edited BasicRecPony.cfg to refer to these new file names. I also made a copy of the Pony directory called BasicRecPony. Then, I edited BasicRecPony.sbs as follows:
Changed last line from %xd(P, %mp)
to %?mp<|||||%xd(Pf)|>
I also commented out the stuff under volume, repeat mode, & shuffle mode since those don't matter to me while recording.
This works fine for me because I'm not using the Sansa Clip to play audio files at the moment. I only use it to record. My status bar changes affect the While Playing Screen, I think. I believe by using the %?cs
tag I can make my changes only affect the recording screen, but I'm not bothering to try that now.