This approach might work fine -- I assume you are using a standard household light bulb. You don't say -- but if there is an inscription on the top of the bulb, it still might show through.
I don't quite under stand your problem, however. The original problem might have been a bad bulb or your enlarger or how they were used together. If there is a problem other than the bulb, your new approach might not solve the "problem". Some enlarger heads allow you to position the bulb. Does yours?
We can only work with the information you give us.
The P211 & P212 bulbs are easy to get here.