Cutting/drilling hole in joist - How big?
If I am visualizing you description correctly... the joist is running parallel on top of the wall, so it is completely supported, thus really carrying no load. I don't see any problem with cutting a temporary access hole, but agree that a round hole is much better than square. Are you sure there are no wires or pipes strapped to the other side of this joist? Be sure to slightly angle the blade of your reciprocating saw so that you are cutting a "tapered" plug that will be removable from your accessible side. When finished, glue the plug back in, and apply a 3/4" plywood sister at least 18" past the hole in both directions. This is actually more cosmetic than structural , but should you happen to sell the house, it will help prevent a notatation from some annoying home inspector about a cut floor joist.