On a 737 you need to go to Flap 15 for single-engine landing due to drag from 30/40 Flap.
May not be necessary depending on several factors. See 737 FCTM page 5.20 under heading "Engine Failure on Final Approach". Basically, it says if the approach is continued and sufficient thrust is available continue the approach with landing flaps.
True, additional to that is the 737 (at least the NG) certified for flaps 30 single engine approaches and landings including CAT IIIa so there is no real performance problem to begin with, at 700 you are a tad late but at 800 you still could do a normal one engine out autoland if you are afraid of your own performance, which of course should never happen in the first place, but that is another topic.