There are some things that cannot be done. It is not likely both computers can use the same program and the same data at the same time unless the program is designed for network operation. Many programs cost more in network versions. No matter that the cord is what inspired the inventor to call it a mouse. A cordless mouse is now being sold by both Microsoft and Logitech, and they are available in most computer stores and office supply superstores.
Installation is simple.
The old mouse is unplugged, and a tiny radio receiver on a cord is plugged in. The cordless mouse can be located as much as 3' from the receiver. The mouse requires batteries, which seem to last indefinitely. They will work fine without the software, but installing it will give extra control over the mouse response. It is not on a par with going barefoot in the park, but there is real freedom in not having the mouse cord snagging things.