By most definitions a GPS is a computer, and they're available in wireless. I use a Garmin Edge 305HR that swaps easily between the tandem and my single bike. Stoker has a Garmin eTrex Legend (no single bike).

I like the Edge because it's so easy to download, save and compare ride data. Stoker likes the eTrex Legend for the display screen that's much larger than a typical bike computer and because the color of the case matches the bike (see below).

The largest adaptive curve in changing from typical bike computers to GPS is dealing with the batteries.

The Edge charges off a plug-in adapter or more typically, the mini USB when I plug it into my laptop. If I don't download and leave it plugged in on Saturday night, it's only about 70/30 if it'll run until the end of the ride on Sunday. If I don't plug it in sometime after Sunday's ride "fagetaboutit" for the next Saturday morning. If I let the battery drain it's no big deal, I still get to go for a bike ride.

The eTrex Legend uses two AA's and gets pretty close to the 18 hours battery life advertised, roughly a set per month if we ride 40 miles every Saturday and Sunday. She keeps a couple of spare sets in the bag under her handle bars and can change them out easily while underway as long as we're not hammering too hard.