Hi,
I also had the same problem as yours. Mine is also a 96 W210.
I think this is a very common fault of 95-97 model W210s

you cannot by-pass that blower regulator. It will not work and the blower might be broken plus it might cost you more $$$ to spend.

The blower regulator for the W210 96 model is not sold anymore and has been discontinued. You may just get the one from the S-class W140. I used that part and it works. It is identical aside from a shorter wiring which can be easily transplanted from the old blower regulator.

I made this conversion a year ago and as of now, it is still OK.

I was suggested by the dealer to change the whole blower and regulator to the updated one but it cost a lot. Got the simpler fix and saved a bundle.

Thanks.