Cordless radar detectors do exist but as far as I know no company makes a cordless version of their "premium" detector - only mid-range models. Cordless detectors never really seem to have caught on - I suspect it's because having to remember to charge them every few days is almost as much of a pain as having to wire a fixed-power detector in.
Detectors also can't go down too much in power draw - superhetrodyne receivers have been a pretty well-explored technology for many years now, and if anything modern receivers will start drawing more power as they gain features like GPS and cell/Internet connectivity.

Beltronics/Escort detectors (they're actually the same parent company now, and share a lot of critical detector electronics - take apart a new high-end Escort and the radio board says Beltronics on it!) and the trusty old V1 are still regarded very highly. There are a few Cobra models that are supposedly acceptable now, but for the most part they are still garbage and I'd stay away from them.

There are a lot of detector review sites online - many are in the pockets of various detector manufacturers but if you sift few a through you can usually start to figure things out. Radartest.com was a good starting point for me as their articles are very well-written and their methods relatively sound, although as the author/owner is both a seller and a contractor for various manufacturers, I sometimes doubt his neutrality.

It's almost impossible to go wrong with a high-end Bel, Passport, or V1 - ultimately I think it mostly boils down to taste. V1 has the arrows, while Bel and Escort now have pretty cool GPS-based filtering abilities.

One thing to make note of is that police are increasingly switching to laser in many states. Laser is a little harder to set up a trap for as the police car needs to be stationary and the cop needs to be looking through the laser gun to aim it (and hence in view of and nearly perpendicular to the road), but it's virtually impossible to detect in time to avoid a ticket. Laser jammers are still legal in a few states, though, and are very effective. I'd do research on laser usage in your state before buying a detector system.