Hi Judie, and welcome aboard. You mentioned your credenza is white...I'm assuming it's painted? As long as it's not bare, unfinished wood, you should be able to get the trivet off without causing any damage, but there's always a chance that it's already damaged underneath the cork.
Anyway, to get the trivet off, I'd suggest puddling a bit of soapy water (using something like Murphy's Oil Soap, a mild dishwashing detergent, or Simple Green) around the edges and letting it soak a few minutes before trying to work it off. Unfortunately, the Vaseline is likely to prevent the soap and water from soaking in, but I think if you can get some soap worked under the cork it'll start to loosen up what's sticking it. Once the trivet is loose, the thorough cleaning with the soapy solution should clean up any remaining residue. At that point, you'll be able to see if the finish on the credenza is messed up. The soapy water shouldn't do any damage itself, though.
But that's just my off-the-hip thoughts. Before you do anything, you should see what other suggestions show up. We have some members who know a lot more about furniture finishes than I do.