I don't know the science of tuning the string from D to E. It might put enough additional tension on the string to cause it to snap or enough additional tension on the neck to be a concern, or maybe not. I hope someone with more knowledge about strings answers that question for you.
If you do tune your tenor banjo to CGEA, you could use the chord shapes for an ukulele with the same tuning. You could no longer use the chord shapes meant for CGDA tuning because you'd end up playing the wrong note on the string that had been changed from D to E. For what it's worth, I bought a tenor guitar, which was developed from tenor banjos and is generally tuned CGDA, like a tenor banjo. I asked the seller to install strings for DGBE tuning (also known as "Chicago tuning" in tenor guitar circles), like a baritone ukulele and like the top four strings of a guitar, so I could use baritone ukulele chord shapes to play it.