I'd use bleach, not trichlor. Trichlor is acidic, and if you get enough on the spot, will damage the plaster. (Doing in a pool that's full is much less risky.)

Bleach will not damage the plaster, as long as it has no organic binders or materials present. With an old pool, that shouldn't be a problem. I'm not sure if acrylics or latex binders are being used in new plaster.

BUT if your plaster is as old and deteriorated as your concern implies, do NOT let it dry out.