Your best bet is just to start having this discussion with a few lenders, to see what your options are and what rates you could get. Scrape & rebuild isn't as common as the typical home purchase, but it's common enough that lenders are ready for it.
Two main options are currently popular. One is an FHA 203(k) loan, the amount they'll lend is based on the projected value of the final home, so you don't have to worry about your current appraised value too much. You could run into trouble if the house you're planning to build won't appraise comparably to other houses in the area given the loan amount you're requesting, but it doesn't sound like a big concern at 200k (an issue if you were wanting to build a $1M home in an area where houses are ~$200k, for example).
The other popular option is a construction to permanent loan, which is basically a construction loan combined with a mortgage. A construction loan, by itself, would typically be payable a short time after construction finishes, so you'd need a mortgage at that point to pay off the construction loan, rolling them together in one construction to permanent loan can lock in a favorable rate if rates are rising, and can save additional closing costs.
Make sure to shop around lenders, especially try to find reviews from people that have done a scrape/rebuild since it's a little different than the workaday mortgage.