Indeed. Operating Uk/Switzerland is not such an issue. From a tax perspective though, you should carefully consider where you create the company, depending on where you are domiciled (notably taxation of salary and dividends) and you will probably end up with having the company incorporated in a country and a branch or representative office in the other. Whether you want to optimize this in a tax way or not, is a question of budget...

But from a legal perspective, to operate as a ski school, there are surely some requirements, so watch carefully for this! Maybe it is easier if you offer a partnership to an existing ski school in exchange of shares/compensation....