It depends on the concentration of what your analysing in the water. Given that it's water, I can't imagine there's an especially high concentration of any organics in there (I assume that's what you're looking at), which means that your unlikely to see anything on GCMS from the DCM extract. DCM is quite easy to remove though, as it is quite volatile (note: DCM is carcinogenic, so evaporation should only be done in a well ventilated area such as a fume hood). Is there no way you can find a lab with a rotary evaporator? It's not completely necessary (unless your compounds aren't stable), but it would expedite things.
What sort of input do you have on your GCMS? As in, is it just fitted for liquid injection, or do you have SPME available? SPME might be a better alternative if you have it, but it depends again on what you're looking at and whether or not you have an appropriate fibre available. Otherwise, perhaps consider dispersive liquid-liquid microextraction with something like MeOH and xylene. This requires less solvent, and you wouldn't have to worry about evaporation. There should be a bit of literature on this, as I think it's quite a common method for analysing the presence of certain plastic residues in water samples.
One other thing. Are you hoping to do quantitative analysis of this extract?