Unfortunately, because we dont know the extended terms of the equity loan (can it change?), or the terms of the mortgage you might get instead, or the closing costs you have been quoted, it is very difficult to answer your question. I suggest you go to a local lender and get a concrete quote for a new mortgage. Then, calculate the cost of that new mortgage (closing costs plus interest for the number of months you think it will be before you pay it off).
Compare that to the cost of carrying the balance on the equity loan for the same number of months.
See which is cheaper. Then, weigh any risk of changing rates or uncertainty of selling, and decide which is the safer/better/least expensive option.
You may have a lot more flexibility as a “cash buyer” of the new property (meaning, no new mortgage needed, even though you are borrowing the money). But, you may find it much harder to carry the debt long term, should you not be able to sell.
Make sure to consider any expenses that may or not be tax deductible in your comparison as well (your local tax pro can help you with that part of it).