The listed chain wrap capacity of the short cage derailleur is 29t, which if you do the math means that as long as you don't shift to a cog smaller than 21t when in the smallest chainring with the setup you describe, you should have the chain wrap capacity to cover it. It's likely you might even be able to go to a smaller cog than that without problems, Shimano tends to be conservative with their spec (they are with the listed large cog capacity anyway, although there are more variables at work there than there are with chain wrap capacity).

The maximum chain wrap capacity requirement is figured as follows: largest chainring teeth minus smallest chainring teeth plus largest cog minus smallest cog. So 50-28+28-13=37. Your max chain wrap capacity requirement is 37t, the short cage derailleur's listed max chain wrap capacity is 29t. When in the smallest chainring and largest cog, you're wrapping 22t of slack, so if the official specs can be believed you've got 7t to spare before the derailleur has wrapped all the slack it can affectively handle, which again, in your case is a 21t cog (28t minus 7t).

You will have spent the money on a new crankset, a new cassette, etc. I'd buy a long cage derailleur and do it right, the situation you describe is exactly why they make long cage derailleurs-