How many fields is too much for a primary key?
First off, don't worry about performance until you're sure you have a performance problem, especially for a tiny number of rows.

Second, whether you use a unique index that is primary key or a unique index that isn't the primary key to enforce the uniqueness of the combination of your four columns the performance will be the same with respect to that index.

Whether to make that unique index the primary key should depend on what else is going on in your schema.  If you have another table (or tables) that reference this table, then your compound primary key is going to get propagated to other tables as a foreign key.  If that is going to happen, they you have more to think about.

If you don't need to worry about propagating a compound foreign key, then you should probably just make your compound unique index the primary key of your table.  That would be the least effort which achieves your goal of enforcing your business rule.