Try not to use a sawzall unless you are really talented with one, they tend to go through the sub floor.
On 1/4 inch thick floor, I use a razor knife and lots of elbow grease. You could also use a flush cut saw or a grinder with a small circular saw blade on it, but be careful.
I have also just left the cut with the inch and a half around the room against the wall with the circular saw. Then installed the new plywood floor up to it if that is a possibility.