Adding affiliation due to a 1-month visit during a salary gap
I don't think that the effect will be different no matter what you put, but the latter (...hospitality...) version seems marginally more honest. Being a visitor at a prestigious place caries some cachet of course. 

I don't think that a one month salary gap is going to be any issue, if it is even noticed. But you will mention the funding agency, of course.