How do you Get a Close Shave when you have brisk whiskers, sensitive skin and take blood thinners?

I had read that the Merkur 30C I own has a head design equivalent to the 34C (which I don't have). I consider it a mild razor and almost indistinguishable from the EJ DE89. I have never cut myself with either using prudence.
I think the equipment you have can deliver the shave you seek. Limit your blade usage numbers so you are always sharp. Keep the blade presentation angle as low to the skin as you can and still cut (some of a buffing movement will help you find the sweet spot). Make sure to use enough soap.
Be well, no bleeding, may the condition requiring blood thinners subside, happy shaving.