A convergent squint will usually correct just as well with contact lenses as with spectacles. However, if vision is bad in the squinting eye, it may not straighten with spectacles or with contact lenses.
The convergent type squint is caused by the need, due to congenital focus error, of excessive efforts in very early infancy to focus far objects this being almost impossible to do without corresponding eye convergence. (The focus and convergence are linked.) This leads to 'crossing' of the visual axes and so the vision of one eye has to be 'suppressed' whilst the other continues to be pointed at the object which would otherwise be seen as double. (Divergent squint is the opposite, there being no need to focus near things the convergence is suppressed leading to an eye pointing outwards and this does not correct so well).
Relieving the need to focus usually relieves the tendency to convergent squint at least as well as with spectacles and in some cases, people will relax and accept more focus help from contact lenses than from spectacle lenses.