You can certainly paddle the boat as is. Personally, I would repair it.
Steve’s idea of a deck replacement would certainly work, but scrapping your entire deck, which appears to be vintage and intact, and replacing it with an entirely new one seems to me to be a lot more work than is necessary. It is the ends of your inwales that are rotted, not the end of your inset deck plate. To repair the rot inside the hull, I would cut across the existing inwales transversely either where they join at the tip of the deck plate, or any place between there and the interior stem of the hull at a location that the wood is sound. That will leave a roughly triangular open area in front of the existing deck plate. Shape a template out of stiff cardboard or thin plywood and shape it to fill the space exactly. Use that as a template to cut out a small deck from any nice looking hardwood that you choose. Leave it slightly oversize and shape it to a precise fit using wood rasps and sandpaper. You are going to have to do this and much more if you choose to fit an entirely new deck plate. You can bond that new end piece to the cut ends of your inwales using a waterproof wood glue or G Flex epoxy (I prefer the latter). Drill a hole at the tip of this new piece so that water can drain from the inverted boat.
The rotted pieces of the outwales are rather easily repaired. Harmony Gear sells a four foot splicing segment of radiused ash gunwale for this type of thing:
One segment will probably suffice. You want the “kerfed” version. The kerf is the thin lip of the outwale that covers over the molded hull. These splicing segments will probably be a bit oversized compared to the existing gunwale but they are easily shaped to be smaller using rasps and sandpaper. For splicing in gunwale segments I and most others use scarf joints which are much easier to cut than shiplap joints and look better IMO. Many builders insist on using very long scarf joints of a 1 : 7 ratio or even greater. This may be necessary when bonding thin panels together to get an adequate bonding surface for adhesive, but for a 3/4" thick gunwale I have found that a 1 : 3 scarf works perfectly well and provides more than enough bonding surface. Again, use either a waterproof wood glue or better, G Flex epoxy. Make sure and seal well any interior surfaces of your new pieces of wood that you are not bonding to.
Here is a pdf file on gunwale repair from Mad River Canoe. Toward the end there is a section of repairing inwales and outwales with splicing segments: