If your froe has showed you the spiral grain, a saw-cut plank goes cross-grain and as a paddle, too weak to be useful.
Make something else from the wood. You break that paddle in the middle of nowhere and you have an instant problem.
You have to put your faith in each and every paddle you use. Don't even think about it.
Every paddle that I've ever seen is beautifully straight grained, even the one that I used to stir 45 gal batches of wine.
Some of the cedar that I carve from shake blocks is quite weathered and potentially sand-dirty from outdoor piled storage.
I need to split off 1/2" or so from all faces to clean it up. My straight froe could use a little bit of a grind for a finer edge
but as for now, it splits very well. Of course, there isn't much else that splits as easily and cleanly as Canadian western red cedar.