Upvote:2
You are staying slightly longer in Switzerland than in Italy, even if you enter through Italy. You could argue that the time in both is "roughly the same" and that you should apply at the Italian embassy because you go there first, or that the time in Switzerland is "somewhat longer" and that you should apply at the Swiss embassy because that is the main destination.
If the Swiss embassy processes your application, they must have agreed that Switzerland is the main destination and they are competent to issue the visa. There will be no problems on entry from that.
If the Swiss embassy declines to process your application and refers you to the Italian embassy, they must have decided that they are not competent to issue the visa.