Yeah it's called skip day. It wouldn't be a day of the week it would literally just be a day with no name attached to it and every four years you'd have two skip days. So you'd have Sunday December 28th, and then 2 days later would be Monday January 1st. As long as we all accept that skip days don't exist within a week it's fine.

It's a little weird but it's only weird for two days or one day rather than being weird basically all the time.

I live on earth, I'm an adult and speak English as my primary language, and even I need to do the little song to work out how many days a given month has.