We're doing essentially that right now. Loan against our current lake home, building a new one, planning to sell the old one and pay off the loan. For us, the cheapest option was a standard first mortgage. About $4K fees and costs and 2.875% interest rate/30 year. It was a huge PITA because of the documentation demands but no major obstacles or excitement. Shop around, fees and rates definitely vary. You are the customer, so behave like one.
A HELOC is almost certainly not an obstacle to selling. At closing, one of the closer's responsibilities is to disburse funds to pay off any encumbrances on the property, then pay the seller the balance. Encumbrances can include a first mortgage, HELOC, mechanics liens, legal judgments, etc. Lots of stuff that the title search may smoke out and HELOC is just one checkbox on the list. These payoffs are necessary for the buyer to receive a clean title.