Mick,
Yes, a lot of people are “allergic” to superglue, I’m one of them. Just one sniff gives me severe hayfever symptoms for 3 days. I don’t think there is any way of desensitizing yourself so the solution is to use alternative adhesives. I find I can use the “odourless” type of superglue without too much trouble but it does need a “kicker” to make it go off really quickly. As you are glueing wood to wood, why not use a proper waterproof wood glue such as Aliphatic or Super Phatic which sets pretty quickly although not with the instant grab of a fast superglue. You may need to temporarily pin or tape the planks in place.
I’m OK with epoxy resins but some people are sensitized to those so it’s rather a matter of luck as to what you can and cannot use.
Colin