The Supply razor, available from Connaught, might suit.Yep even with the Softguard although I found it slightly better than the others, but still too much.
I've not tried an injector, are there any modern ones? Really don't want anything used.
It has 3 replaceable heads for mild - medium - aggressive adjustment and is a nice device. I tried one and sold it on because, although it worked very well, I didn't actually feel anything happening - the bristles just went away. This might well suit you with the mild head fitted.. One can sometimes find new old stock Schick Adjustables on eBay but they tend to be expensive for what you get. The clone of the Schick Type 'L' from PAA gets poor reviews.
Good luck with your quest.