It's better to simply get an appraisal. Do NOT supply the intended purchase price to the appraiser, as you would for a mortgage. If you give the appraiser a target price, they will try to justify it. Our neighbor's house appraised for $425k, because that is what they offered. This was one week after we bought our house for $340k, and got an appraisal at that price. Thing is, our two houses are identical in size and layout - they are two of five all built at the same time as a tract. The appraiser even came over to talk with us, saying he had a hard time making it work, but he did.
Your offer is stronger when it is not contingent on a mortgage, by the way. It can still be contingent on an appraisal. And while you're at it, might as well make it contingent on a professional home inspection.