Is better if you recreate the product.
The attribute set defines product parameters (all the attributes) and you can't really modify all those relations.
Even if you change the attribute set id inside the database, you will have to remove garbage entries of previous attribute set.
There are some third party extensions that allow you to convert one attribute set to another, but even with them it won't be a clean process.
Usually is easier (and cheaper) just to create your product again.