So a standard 10 gallon measures
12.5"H x 10.5"W x 20.25"L
assuming the water height will be set between 5"-8" of water at the very least it will leave 4.5x10.5x20.25 which will be able to hold roughly a extra 4 gallon of water.
I would go with a sump. I was in the same position back in the day, and glad I did to this day.
Do a little research, try and go with a slightly bigger DT if possible, and go about it all in a calculated/methodical manner. It's easy once the physics are understood.