(Not a teacher)
To me 'wriggler' sounds like an affectionate term, talking about a baby, or a pet. From the verb 'wriggle', describing movement. If it's a pet, it would mean that whenever you tried to pick it up it would try to free itself by wriggling it's body. If it's a baby, then it's describing how the baby moves it's limbs.
That's what I'd say at least. 'Wee' is most likely 'little/small'. In Scotland, 'wee' is used almost exclusively in place of 'little/small' among speakers.
What I took from the 'Why he even denied it anyway' sentence, is that a person has denied ownership of said 'wee wriggler'. What that is, exactly, I don't know - his daughter? his pet gerbil?