I would agree if you think this will be the only project you will undertake with an AR rifle. If you think that you may want to start building your own in the future then investing in the tools wouldn't be a bad idea.
To complete this project you will need at least a barrel wrench, barrel vice blocks/action blocks, hammer, correct size punches. The manual recommends that you torque the barrel nut; so if you follow that you will also need a torque wrench. You can easily go over $100 getting this stuff. If you want to save yourself an embarrassing trip to the local gunsmith as you said, well it may cost you a little bit to do so. You probably can get this job done for under $50 almost anywhere. I guess you have to figure out what is going to take a hit more, your pride or your wallet.