I have a MinnKota 35 lb. thrust motor that I have run from a home-built PWM controller for more than thirty years. For most of the use, power drain is minimal and an 85 amp-hr battery is good for a couple of days. Running at full power can drain a battery fairly quickly though. I don't recall the current demand off hand but I believe that it is in the 30+ amp range. I experienced that a couple of years ago when I was fighting a heavy wind and after a half an hour of running, there wasn't enough left in the battery to start the outboard.
Most cordless power tools are good for 2 - 3 amp-hrs. A set of four would provide around 12 amp-hrs which would drain fairly quickly.
I would consider rechargeable lithium cells for the highest energy/weight ratio. 18650 cells, the type common to laptops, are a possibility. However, particular consideration to balancing the cells and fire protection. Other cell configurations are possible as well.