Sony Playstation 1 for a CD player ???

no, not at all, you just hit the start button to play/pause, r1 to skip forward a track, r2 to fast forward (which it does very fast, which i like), and select to stop.

when it's hooked up to a tv it does show the time elapsed and number of tracks on the disc, but i never bother with that.

As I've found (and bought) there are cheap wireless controllers out there. I found one on ebay for $5. Having a remote removes the only thing I wouldn't be able to deal with -- using a wired controller that isn't long enough to reach my listening position.

Does the DVD remote for PS2 also work for CD navigation for PS1? The wired controllers for PS1 and PS2 are largely compatible so I assume the DVD remote is also compatible, but I want to make sure before buying one.

If you're asking me, I don't know.

my ps2 remote did NOT work, but if i remember correctly, there are some that do, though i'm not sure if they are still available new anymore. the one i have (and which does not work on the ps1) is the official sony ps2 remote.