I was thinking about this earlier and it hit me their is a cheaper corner chisel. Whiteside makes an excellent small corner chisel that would work well in this senario, should run $20 or so. You will still need to use a chisel or similar implement to cut the waste out from the bottom.
As for chisels in general I have used them all, from Blue Spruce to Harbor Freight specials, save the new Lee Valley PM versions. Lie Nielson makes an excellent chisel and even at their price I suggest them to new hand tool workers since they come ready to use out of the box. If you don't have a mentor it is hard to know what a good chisel can do until you have had one in your hands. That said most people, even long time woodworkers don't want to pop for Blue Spruce or LN chisels. By far the best value in western chisels are Narex, Highland and Lee Valley both sell them but I would go with the imperial bench chisels from Lee Valley (Highland only has the metric last time I checked). That and one of the sharpening kits from Lee Valley (I would go with the one with the Veritas MkII jig) and one can do a lot. If you want to save even more money on sharpening google scary sharp and look at the sandpaper sharpening approach. On my point about imperial bench chisels vs metric, with a bench chisel it makes no difference really but with the option I tend to go with imperial.
Sorby and LN sell good corner chisels but the Whiteside would be the cheapest way to have a corner chisel that would work well here. If you decide on one of these small corner chisels do NOT get one of the cheaper versions like Porter Cable and Grizzly sell both are garbage IMHO.
Even the most ardent power tool woodworker needs some good handtools, the three essentials that pop to mind are a small set (4) bench chisels, scrapers and a high angle block plane. I do caution as handtools can be a vortex for money, the next thing you know you will have 20 hand planes, a wall full of saws, 30+ chisels and be arguing over oil stones, water stones and diamond stones... You know you are completely off the deep end when you have a 2 and three jaw brace, actually use gimlets, start a rounds and hollows collection and start thinking of taking out a second mortgage to have Karl Holtey build you a custom infill plane... http://www.holteyplanes.com/
One other thought if you happen to have access to a square chisel mortiser you can use that to square the edges. Ha I figured out a way to use a power tool after all.