I am personally of the belief that if you cannot take a hot shower first and only have time to shave at the sink then that is the perfect moment for a pre-shave cream such as made by Proraso or 3P or perhaps some pre-shave oil. I have tried the wet towel/washcloth technique sans shower and for my tough wiry beard it just took too damn long to get good results. As a note, this is the only time I feel a pre-shave cream/oil treatment is necessary. YMMV.
I'm new here, but can I make a little suggestion - something that I tried the other day and it worked wonders.
The issue I had with a hot wet towel is that it would lose it's heat very quickly as the water evaporated. So I took a flexible wine cooler sleeve and instead of freezing it, heated it in hot water. I figured the gel inside must be designed to hold its temperature somewhat, so surely should work the other way too. I wrapped a hot, somewhat damp (but not wet) towel around it and moulded that over my face and it worked wonders. Kept the towel nice and hot and moist for several minutes while I sat back in a little slice of nirvana.
You could also substitute the wine cooler for 2 or 3 of those gel ice packs I suppose.