What you are suggesting with a back-feed cord is possible, but not recommend for a bunch of reasons, including the ones you mentioned.
The first thing that comes to mind in terms of simplicity is replacing the power wire on the water heater with a cord made for a dryer and plug it in to the generator. When your power crisis is over, you can either wire the hot water heater back, or install an outlet.
The next best thing to do is to buy a transfer switch sub-panel, install it, and move the circuits you want to keep using to that sub-panel.
Many laptop cords are standardized. Where there is no external power supply, they often just need a stock AC cord such as this.
If it is three prong, it may be like this.
If it is damaged, replace it. It is cheap, available at many locations and safe. Do not repair except as an emergency measure.
However, many laptops have an AC cord (the cord that plugs into the wall) that also plugs in on the other end to a power supply (a small plastic brick). The AC wire almost always can be disconnected from the unit and the same replacement technique applies.
The AC cord is on the left, the power supply and its cord on the right.
If the AC cord is damaged, replace the cord.
If the other wire attached to this unit (the wire that goes to the computer rather than the wall) is damaged, this is much more problematic. These wires are almost always not detachable from the power supply, and they are usually proprietary (non-standard connectors). If the damage is very minor, you may be able to get away with shrink tubing, if it fits over the connector (sounds doubtful), or plastic electrical tape (always a bit sketchy on a wire that flexes). This is a low voltage wire, but it still is problematic. You may need to get a replacement power supply from the manufacturer or a third party supplier.
On the other cords, there are two types of replacement plugs, screw on and piercing.
Pierce seems easier, but screw on seems more reliable. They are also available in polarized and three prong versions. Cut the wire above the bad section and bring your old plug to match.
Best Answer
By all common sense you should not try to splice an appliance cord to make it longer. What you should really do is to open up the appliance and remove the remaining chewed off chunck of cord. This may require you to free any type of cord retainers and / or strain reliefs.
Then a new cord of ratings same as the original should be installed in place of the old one. It can be very handy to purchase a ready made extension cord that has nice molded ends on it (rated properly of course) and cut the socket end off of it and use the remaining part to wire into the heater.
Sometimes you will find that inside the appliance the wires may be attached with some type of crimp on terminals. These types of terminals are generally available at hardware stores but if you cannot find exactly what you need check online at retailers such as Digikey or Mouser.