Wireless over-ears with a similar sound signature to AKG K550 mk1

Does something like that exist? Could be either bluetooth or use its own 2.4ghz dongle.

There's nothing particularly special about my setup. The K550 is just plugged into my mobo's Line Out and has done so for 4 different computers over the years. However, I've been thinking about the convenience of having something wireless, since accidently tugging on the wires because of accidently reaching too far to grab something has happened a bit too often.

Main consideration is it sounds similar to the K550 mk1. I think it's supposed to be a relatively flat/neutral signature; it literally says "Reference Headphones" on it for what it's worth. Doesn't have to be exactly alike, just close to and I don't mind if it needs EQ tuning to do so.

However, if it does need an EQ profile then it must be able to save it inside the headphone itself - ie. does not depend on some programme/app actively running on the device.

There's no specific budget, but for reference I paid about £100 for my K550. All usage will be pretty much home/indoor, except maybe very occasionally in the garden with laptop. ANC/mic are not important.

I don't even know if the K550 mk1 are considered good audiophile headphones, nor can I even remember whether I bought them 14 or 15 years ago. But they're just what I'm used to now and it's that sort of continuity I'm looking for, but wireless.