KeithRB:
Actually, I think the slide projector might be AC. My notes from my 1983 senior project state that a Kodak Carosel uses a 25V AC signal to switch. I used a relay, but you may be able to use a TRIAC based optocoupler like the MOC3010. The optocoupler cannot handle the current to switch it.
In situations like this, where you are interfacing with an existing circuit, I think a relay is usually the right choice. A relay is much more likely to work in a variety of circumstances where an optocoupler will fail. I am a big fan of the CPC1218 (normally-open) and CPC1219 (normally-closed) solid state relays, because they avoid all of the mechanical problems that can occur with reed switches. As long as your load signal is less than 600 mA--and, surely it is--I think one of them will work for you.
If, for example, you were needing to pass a high-frequency signal through the optocoupler, a relay wouldn't be the right choice. If you needed to linearly pass an analog signal through, a relay wouldn't be the right choice. But for simply replacing a manual switch with a computer-controlled switch: relay every time.