Welcome to the forum!

this was one of my main problems with WILDs (I don't really try to WILD anymore anyhow)
Try to lay on your side so the saliva can drip out, or, when you are WILDing, just don't think about it, just focus on your goal.
I find that when I meditate, I barely ever swallow...why? because I'm not focusing about not swallowing, then when I think "I haven't swallowed in a while, cool!" I swallow
so just try to focus on the WILD itself