Hi, I'm converting two bikes from cottered crank to Square taper.
First bike is an old German "MARS Markenrad", second is a "prophete Clipper".

They both have threadless BB shells with press in cups.
Where can I find a threadless BB? I have converted one using a threadless BB by german BB manufacturer "F.A.G.". It was a real cowboy job as the two parts of the BB do not srew together, they are both pressed into the shell. In my case I have no press, so I used the traditional Hammer and two by four method. I don't want to repeat this, so I'm looking for a better BB. The original press in cups for the cottered crankset appear to have an outer diameter of 40mm, which is bigger than most square taper BBs. Whenever I go on the internet to find a new BB i can only find info on the shell width, spindle length and maybe the thread pitch, not the cup outer diameter. Am I missing somthing here? Are my measuring calipers broken? Does this 40mm size exist?

Thanks
Colin