In the US you really can't get most accounting jobs without an accounting degree, and the majority will require a CPA for any real progression. There are some accounting jobs that are little more than book keeping that one can get without an accounting degree, but those are best avoided.
The only requirement to work as an actuary in the US are the actuarial designations, which do not require a college degree. However, they do require a lot of mathematical background. No one I know has ever heard of anyone becoming a credentialled actuary without a college degree.
IMNSHO, neither of those professions belong in trade schools in the US.