Thank you for your recommendations everyone, I may be trialling many of them.
Google Maps
Google Maps has an incognito mode if you can't live without, but would like to mimimise the data sharing:
You now have more ways to control your privacy on Google Maps. Use Incognito mode when you don’t want your activity—like the places you search for or navigate to—to be saved to your Google Account.&nb
support.google.com
There are other data controls too:
myaccount.google.com
Remember the time the Google's Mapping cars collected all of the wifi network information of the entire UK? "It was a mistake", Google said, and apologised. Which makes everything ok. Google, Facebook and their entire colossal data slurping mob keep making "Mistakes" and apologising. Controls like that mean nothing. Both Google and Apple have been caught with their pants down, by a researcher recently:
Search giant insists it's necessary, iTitan didn't have anything to say
www.theregister.com
The GSM standard alone, is leaky enough - never mind what OS and App developers get up to. I have a mind to delete Google's Android, and replace it with LineageOS:
en.wikipedia.org
Google Maps is of course excellent on a PC or laptop, but on a mobile - not being able to use the mouse to drag routes to adjust, is limiting. I could of course use my miniscule laptop (it has a sim card slot, 8" screen, digital compass) on the road - it has a mouse-joystick in the keyboard, bluetooth phased array GPS (plus A-GPS via cellular):
en.wikipedia.org
... but then I'd have to fashion a waterproofed mount, and replace it's miniscule mechanical hard drive with a more robust solid state disk.
Or I could use my even older Dell Axim:
en.wikipedia.org
... with TomTom navigation, phased array GPS receiver (slow to get position, because it's GPS only - no A-GPS) and (out of date) maps of the entire world - if the battery hasn't died. Let's hope that one of the many alternatives listed above works well for me.
I like the fact that Cyclestreets is browser based - less data slurpage, but I don't like that it keeps suggesting long dark canal tunnels. And you can't adjust routes.
While trying Osmand+, I've discovered that I can easily save favourite places, without sharing my routes with all and sundry (my enemies are many...) - in that respect it's very similar to the old version of CoPilot, which I very much liked. Open Source and offline maps too - handy for data dead spots. It's great that it shows green areas on the map, as well as roads, so I can segway for oxygen... If I could get it to avoid specific roundabouts, it'd be even better - I don't like journeys which involve going around large busy roundabouts, unless it's the very first exit that I need. I admit, it's a niche requirement, but it's my requirement.
I've also got Komoot loaded, but it doesn't have the "Avoid Road" function (which can be used to avoid a horrible great big bone crunching roundabout, that I might need the 2nd, third or 4th exit of) that Osmand+ does, plus where the hell is it sharing my journey anyway? Can I save a journey without sharing it, on it's own little social network? I just want a good cyling navigation app, I have no interest in any sort of social networking. I'm not even on Faecesbook or Linkedin-to-Microsoft. As far as the antisocial networks are concerned, I'm like Kendo Nagasaki:
en.wikipedia.org
..plus Komoot's "Regions" are too small and stingy.