Its not uncommon for someone to be an independent contractor at an established business. Just ensure that you are properly considered one, and not an employee. Independent contractors make their own hours and essentially call their own shots, which is not unrealistic for tattoo professionals. If you worked at a restaurant or in an office, it would be different.
If you are rightfully considered an independent contractor, you own your own business for tax purposes just as much as the owner of the tattoo parlor does. Their business is no doubt more substantial and complex, but you are treated as a business owner all the same.
Just ensure that the expenses are your own, like your supplies and your products.