Is it safe to save seed from edible peas grown near toxic sweet peas?

This is my first post so I hope it is in the correct forum.

I am planning to grow some "Victorian Colossal Climbing Peas" (Pisum sativum) and I would love to be able to save the seed from them to grow next year. However, there will also be some non-edible sweet peas (Lathyrus odoratus) growing in the same garden.

Can anyone tell me if there is a danger of the two types cross-pollinating? Would this make the edible peas unsafe to eat? I have read that if cross-pollination did occur, then the Pisum sativum seeds would be safe to eat this year, but any plants grown from these seeds next year may produce poisonous peas. Is there any truth in this?

Given that they are in two different Genus (Pisum vs Lathyrus), I don't see them cross pollinating.

Thanks!