Just pay logitech $5/piece to license the patent and then sell them for $200, there is plenty of meat on the bone for everyone involved.

Or bypass the idea of the patent altogether by making their mouse charge wirelessly and then releasing a giant wireless charger that happens to work pretty well as a mouse pad later.

Option 1 only works if Logitech plays ball. They might consider the exclusivity very valuable and be unwilling to license it for anything reasonable.

Option 2 is a great way to land in court. It's one thing to steal IP from a tiny company or individual but Logitech can afford lawyers.