For a good while the two main contenders for me have been Locus Maps and Oruxmaps. Both decent. I trust the developer of Oryxmaps having had an email exchange with him some years ago, but it's not well designed in usability terms. There's an older free version available which can be directly installed - because I trust the developer I do this (in theory a risky thing).
Both of these work nicely with Openandromaps downloads. These are from a different team of people - and can be used in all sorts of apps. These are free. Drawn from Openstreetmap data of course.
The reason this is a good solution is that you can change the style of the map - quite radically. There are lots of different styles available - called 'themes'.
All of which means you have a mapping app which doesn't need to get its maps from the internet - they're all on the phone. And (subject to the details already discussed) if you're just using the normal GPS signal the phone signal is irrelevant.
BUT I agree, this all requires a bit of setup. Not particularly complex, just multi-stage. Downloading maps, downloading map styles ('themes'), unzipping the downloaded files, telling the app where the maps and where the themes are stored.
And learning how to use the interface of that app - not least as you try to tell the app about the maps. This can get messy and hugely irritating.
Then there's definitely the thing about the phone putting apps to sleep to look out for.
Worth it if none of the above sounds too scary.
Also... after many years, have learned that nothing is static in internet land. There may be new apps emerge. Either Oruxmaps or Locus recently announced some kind of subscription service (can't remember which). There may be new sources of offline maps which I've not seen.
OR - if you like, find a simpler tracking app which doesn't show maps at all. There are lots and lots of these. Some well designed, some with adverts, some rubbish. Key for me is to be able to control how often the GPS points are plotted.
(Other apps are available if you're prepared to pay - some of these are probably pretty good - I like the free solutions!)