I don't think I've ever seen a marshmallow recipe without corn syrup, except maybe for methocel marshmallows. But assuming these are standard gelatin marshmallows, you can dredge them in confectioner's sugar and that will make them easier to work with.
Don't "dust" them, actually dredge them, otherwise you'll just end up with globs of wet sugar attached to the exterior. This might happen anyway if your marshmallows are particularly watery, so you might need to dredge them a few times.
Also, don't cover them; it's important to let any moisture evaporate. Gelatin is pretty stable as a gelling agent, but fresh marshmallows are still prone to syneresis, and if you leave them in an enclosed container, the condensation will cause more problems.
If worse comes to worst and the sugar doesn't help, just leave them out in the open for a longer period. The water will continue to evaporate over time and eventually they will reach the consistency you want - although they might shrink a fair amount before then.