"Jim G" wrote...
... mini stereo system (Panasonic SCM PM39D,
http://www.jr.com/JRProductPage.process?Product=3985852),

...stereo mini plug adapter...(... "Option 2":
http://www.pcstereolink.com/stereocomputer.html).

Can any of you tell me whether this sort of adapter involves
any signal degradation

Unlikely any that you would hear on your mini system.

compared to a normal Y-adapter?

It *is* a Y-adapter. Dunno why it would be any different
than a "normal" one (whatever that is?)

Also, I'm thinking it might be more flexible to use an
adapter that terminates in female RCAs and then use an
extended Male-to-Male RCA cable to go the rest of the
way. Since this uses an additional coupling, does it entail
signal loss or weakening?

Not unless the connectors are falling apart. 95% of the quality
of the sound is those speakers. You are worrying about 1/10
of one percent. I wouldn't even give it a second thought.

There is a small possibility that the computer sound card
won't like driving both the computer speakers AND the
input to your mini system, but even that is a 2% chance,
very unlikely in my opinion.