Appraisals really are for 3rd parties to guess at the value.
I hope that if you are buying a house cash, that your realtor has given you an idea of value and that you have seen enough houses to have a good idea of the value.
Now your realtor could recommend an appraiser.... but chances are you've seen more homes in the immediate area, recently than they have and may have a better idea of values then they do. Most appraisers work a very large area and not the tight radius a buyer might look. That's why your knowledge may be as good or better than theirs.
They're also looking at the same CMA or printouts that your realtor would give you.