I recall installing only one fixture requiring type B lamps. Owners had purchased all the fixtures for the new house. If your fixtures are not enclosed and the 40 watt Type B will physically fit in the available space, that should be OK if the brightness is not an issue. If enclosed fixture, the maximum wattage should be posted on/in the fixture. If the CA will fit and is in the acceptable wattage range, I see no reason not to use it.

These are just small bedside lamps. I guess they are "accent lamps." One has an upright shade, so there is no risk of touching. The other has a sideways shade (like those green banker's lamps but smaller). That one does not have much space in it for a bulb. DH has a 40-W type B in it right now b/c it was the only thing he could find that fit. I would like to put a 25W bulb in b/c the 40 is too bright and I am a bit concerned about the heat output. I will try to find a 25W CA bulb that is short enough. I wish he had kept the old bulb when he changed it so I could see it. I think it might have been the bulb that came with the lamp long ago.

Anyway, thanks for the advice! It seemed like the CA *should* be an option, but I wanted to hear someone else say that too.

If the B- 40 fits, then you can use it to compare lengths. Please tell us the base size of the lamp. Edison (standard for 60 and 100 watt), candelabra ?
Plenty of 25 watt Type B are available with the candelabra base, the GE Reveal line being an example. Adapters from Edison to candelabra are available on eBay and would add negligible length to the assembly. For those with more experience, changing to a different socket type would be possible.