First - what do the faces look like?
Square is a correlation between two faces - so the first thing you need is a flat face before you can get a square edge. This is still doable without a jointer & planer (though those two tools make it a breeze). You can hand plane one face close enough to flat so it won't rock on the table saw table and then square up the edge as you describe. But if the faces aren't true, the quality and safety of using anything on the edge is questionable.
If you've got one good flat face, then both methods you describe will work - for the router table, you need an offset fence that has the infeed side set back to allow for the depth of cut and the outfeed side is flush with the cutters. For the TS, sticking it to a known straight board and running it through works great. As long as the board is flat on one face, these methods work great.