for fear that someone/something "would" or "should"

[sunsunmoon]

https://www.usingenglish.com/forum/ask-teacher/54082-less-fear-might-rain.html
I took an umbrella with me for fear that it would rain. (I wouldn't use "should" there. Perhaps that is an AE/BE difference.)

1. ...for fear that it would rain.
2. ...for fear that it should rain.

Do BrE speakers prefer #2 to #1? Is #2 unacceptable in U.S. English?

 

[5jj]

The whole thing sounds a little old-fashioned to me whatever modal you choose.

I'd probably me more likely to say, "in case it rained"