Since this is such a small area you could get it done by renting just an edge sander. Then you would sand over it with a 36 grit, then again with a 50 grit, and finally with a 100 grit. Then you may want to even take a palm sander over the entire area to make sure you get out any swirls left by the edge sander. Then wipe down with water, let dry and apply stain using a deck pad. The stain will take the longest to dry, but you could just plan for this to where it is during a least inconvenient time. Then use a waterbased finish such as Bona traffic, and you can do all the coatings in just a few hours... Another option might be Rubio Monocoat, it is color and finish in one application. Check them out here http://www.rubiomonocoatonline.com
Hope this helps.