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Join Date: Aug 2010
Location: Madison, WI
Posts: 11,203
Bikes: 1961 Ideor, 1966 Perfekt 3 Speed AB Hub, 1994 Bridgestone MB-6, 2006 Airnimal Joey, 2009 Thorn Sherpa, 2013 Thorn Nomad MkII, 2015 VO Pass Hunter, 2017 Lynskey Backroad, 2017 Raleigh Gran Prix, 1980s Bianchi Mixte on a trainer. Others are now gone.
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I bought my first GPS in 2001. It met all your criteria, the basic Garmin first version Etrex. But I do not know if anyone makes anything with that little functionality any more. But I doubt that you would be able to find the 20 year old handlebar brackets that you would need to mount it, and the handlebar brackets would be 26mm, not 31.8mm.
It had no internal map and I do not recall if you could attach it to a computer or not, but if you could it would use the proprietary Garmin plug on an RS232 port, that was before USB existed. It used AA batteries. I bought it for kayaking on Lake Superior, I manually entered the lattitude and longitude coordinates for campsites so if the fog came in while I was kayaking towards an island, I would not accidently miss the island I was paddling towards.
If you do not find exactly what you are looking for, you could look for any vintage GPS that is small and has the handlebar brackets available, as they all have had the functionality that you want. They all used AA or AAA batteries, so you do not need to worry about a proprietary Li Ion battery that won't take a charge any more. I use rechargeable NiMH AA batteries for that sort of thing, the white Ikea Ladda or Eneloop rechargables are the best batteries to get. But they might have lost their waterproofing.