Why can’t the wall be funded via the Pentagon Funding? It is a defensive measure. National Defense is the purview of the Department of Defense.
Furthermore, the Army Corps of Engineers would be the natural manager of the contractors building the wall. They managed the ALCAN Highway. This would be a hell of a lot easier!
I think, after Trump gives Congress a chance to do it the “right” way, he will indeed just get to it through a number of other measures within his authority.