Having a dealer register the gun will still require it to be engraved (that isn't free), You will have to pay the transfer (AOW is $5) and pay dealer their fee for the transfer (anywhere between $25 and $100 depending on the dealer). AAAAnnnnddd you won't get your gun back for 6 months while the transfer is pending.
You can do it yourself. File a form 1, Pay the $200 to register a new NFA firearm. Get the gun engraved. Wait 6 months for the form to come back. Once the approved form and tax stamp is in hand, put all the foregrip you want on that thing.
Can't say which one will be cheaper, they will both take half a year, but if you do it your self, you get to keep your gun (but for the love of God, don't put that grip on till you get that approved form!)