About 18 years ago I had to go on blood thinners for a genetic clotting disorder. I did some research and bought a Braun. I used the same 18 year old shaver this morning. I replaced the blades about 10 years ago. I've got no complaints. It provides a great shave with very little effort. Originally it took about a month to figure out which way to shave (or train my beard). I took a quick look at the Braun website and the shaver I haven't isn't available anymore. The styles have changed but the basic head is the same. I will only add that I don't have a thick beard or one that grows very fast. I can forget to shave and no one notices except for me when I rub my hand across my face.
You didn't ask for this next part so feel free to quit reading. When I was first told to get on blood thinners I had a similar reaction to your opening post. As it turned out, for me, it was an over-reaction. The thinners basically brought my blood to a normal coagulation level. The first time I cut my self I didn't bleed out. I don't know what your ailment is or what medication you have to take, but, based on how much you enjoy shaving, it could be worth it to see the effects of the thinners before changing your lifestyle and investing in an electric shaver. I was Warfarin for about 16 years and just recently switched to Xarelto.