Since wire bodies are bodies of 1 entity, turns out you can just get the first and only edge within, using IBody2::GetEdges(), select that. Whether it's displayed, or set to non-selectable matters not.
Feel free to chime in if anybody's got a better solution without making selections, as most of the other IModeler methods works with just Curves and points, no selections necessary
I haven't found the good alternative to your solution. But the good thing is you do not need to display this body and you can use API only selection to preselect those objects. So basically this behaves exactly in the same way as is passing the curves (i.e. none of the current user selections affect the sweep operation and no selection or temp bodies are displayed while the sweep operation). You can follow this example: Create Elliptical Swept Temp Body