Hi Alexandre -
Generally there is not a lot of difference, but in this case 'for' sounds better.
The joke does not work FOR me. <<---- This is the usual expression. If you change the word order a little bit by adding 'at least', like you did in your notebook entry, then you should still use FOR.
The joke does not work FOR me.
The joke does not work, as least FOR me.
I hope this helps.