You seem to be comfortable enough to want to repair the cord instead of just pitching the pump & buying a new one, so I'd suggest that you completely replace the cord.
Open the pump up, detach the existing cord from the pump entirely, then replace it with a longer length of equivalent cordage all the way from inside the pump to the plug.
You'll have to read the labeling on the cord to know what type of cord and also what AWG it is. You'll need to use the same type and the same or larger AWG. For example if the current cord is 14 AWG, you'll need to use 14 AWG cord, but you could also use 12 AWG (which is a thicker actual wire), so long as the new cordage will fit through the water-tight seal on the pump.
You'll also need a water-tight, outdoor rated plug to put on the other end.
When you're doing this, you can buy as many feet of cord as you want so that you've got one unbroken run from pump to plug.