If you see bare wire I wouldn't do it. If the inner insulation is good I would cut the end off the cord so I could install the proper heat shrink tube over it, and then install a new plug end. And also likely use a gfi on the skimmer outlet.
Coat the wire in liquid elliptical tape then used heat shrinks over the liquid elliptical tape
Like this stuff it’s what I use on all my marine boat wiring
I may try one of these remedies but I’m a little concerned. May be more prudent to wait on the replacement pump to return to stock. Would hate to spend all of this time setting this tank up just write to nuke it or my house