Yeah if its wireless, there's less chance it will have auto restart. Every one I have had thats wired, has always had that feature.
One of the cheapest wireless ones (Sunding 563) is pretty clever, it has a motion sensor (which makes it sound like the unit is broke when it isn't). This same one also lights up if it is too dark to read. No pressing the light on, no daft thing where it only lights up after 6 PM (like another one I have does), it has a light sensor built in and knows if you can read it or not! I have to laugh at this since it probably cost around £8.00 delivered from China brand new.
The downside to that Sunding one is, it got a fault where if I ride 10 miles it will say it was 6 miles. If I do 20 miles it will say I did 12 miles etc. It did it out of the blue one day after registering the right distance for months. This one is also horrendously cheap to touch and has very nasty hard plastic buttons that are as loud as a silver-back gorilla up-gearing under load. The
buttons at least for now, still work.

That one registering only 3 miles out of every 5 is the reason I am back on the one without any auto-on feature. This is why people spend five times more on Garmin's with half the amount of features.
China sells ones like Cateye, but its usually slightly more costly than it is to just get that same one here.
When two cyclists get married, they should throw anodized cable crimps instead of confetti.