Thanks to Phlume for pointing me towards these via the previous cheap Dell mouse deal. While browsing the site I also came across this basic 3-button wireless mouse that can connect to multiple devices using either the supplied 2.4GHz USB receiver or Bluetooth. The reviews are generally positive so I'm guessing they're not awful to use.
If you lose your receiver don't despair you can get a replacement for only $7.80! The documentation doesn't state it but if these work similar to the Logitech Unifying Receiver (or if they're made by Logitech) then you may be able to plug a separate receiver into different computers and connect your mouse to more than one. That way you can carry your mouse around with you and not have to worry about plugging the receiver in each time you change location (and them promptly forgetting it when you leave).
Since these are genuine sale prices on the Dell web site without the need to enter a code you should be able to take advantage of your favourite flavour of cashback as well, plus any associated coupons or discounts they offer.