To directly answer the question asked, you only rewire one side to make a crossover cable. Making a crossover cable from a patch cable is simply the act of swapping the destination of two pairs of wires in the cable. Doing that to both ends will result in a (nearly) standard patch cable again (of course two of the wire colors would now be swapped but the functionality would be that of a patch cable).
In the early to mid 90s there was very little need for crossover cables. They were basically only used when creating peer-to-peer connections between just two devices or connecting anything to a router. For the last 10-15 years practically every router, switch, hub or nic you can buy has Auto_MDI-X which eliminates the need for crossover cables entirely. This feature is also only needed on one end of the connection so even devices which don't support this feature won't need a crossover cable if they are connecting to something that does have it.
Even if Auto MDI-X didn't exist, (almost) all home routers have builtin switches and that means you'd use a regular patch cable to connect to it. IMHO, you should probably just get rid of all of your crossover cables because it does exist and it is almost universal at this point. Even if you only have a single device on your network (which I strongly doubt is the case), it's still much better to have a switch on your network than to connect your one device directly to a single port router. With a switch you can easily add new devices as needed without unplugging the old ones.