If you don't mind drilling holes (tool needed, hand drill, either power or manual) in the shafts of the paddles, you can construct a simple brace/bracket that will minimize the holes drilled into the wall.
The bracket would be two pieces of wood, crossed at the desired angle. Holes drilled at the ends would accept dowels of appropriate diameter, glued in place. Make the dowels long enough to go nearly all the way through the paddle shafts, but not quite.
It would be a good work flow to build the crossed pieces from two layers, as you don't have a dado blade for the table saw you don't have. You can then join them in a cross and have the same level for the dowels.
Drill fairly small holes in the ends, not dowel sized, and place the cross-bracket on the paddles. Mark through the holes onto the paddle shafts to enable you to accurately drill for the dowels.
You would purchase a paddle bit for best results, although a more expensive forstner bit will also suffice.
Note in the picture above that the paddle bit has a center spur. You would not want to drill into the paddle shaft so deeply that the spur extends to the other side.
A Forstner bit has a smaller spur and also would produce a cleaner hole, but is two to three times more expensive, unless you buy lower quality drill bits. I did, once.
Both of these are one inch diameter bits. You would use one inch diameter wood dowels cut to the necessary length and glue them in the holes drilled in the aforementioned brackets. There will be some slop depending on how steady you are with the drill. Urethane glue (Gorilla glue) will expand to remove some of the play. Once cured you would drill through the bracket for wall mounting and of course, drill the matching holes on the paddles.
You could also approach the work flow by moving the bracket over the paddles after having drilled the holes but prior to applying the glue and using the bracket as a template/frame to hold the drill, drilling through the bracket into the paddle shafts, to ensure alignment.
Note also that the paddle shafts will engage the bracket at different levels and the dowels for the outer shaft will have to be longer than the dowels for the inner shaft.
It will be necessary to use some adhesive method to hold the paddle shafts to the bracket. I think the 3M Command Adhesive strips are your best bet there. They can be removed when necessary and will hide behind the shaft.
