How would a hangover be a problem at say 10am?
I am asking these questions because this is the approach that the court will take
The law says that a child is entitled to ocntact with both parents and the courts will enforce this if necessary
Nothing that you have said suggests that supervised ocntact is likely to be ordered - and if it is it certainly cannot be supervised by you
This does not mean that your concerns are not important - just that they can be managed in a way that keeps the child safe - so 10 until 4 on a saturday with hand overs at a local Contact Centre could work.
If he turned up drunk the centre would record it, refuse the ocntact and provide you with evidence of the problem.
Your starting point is to try and discuss matters with your ex using Family Mediation
If your ex will not accept your offer then you would have little to fear as the offer would be seen as reasonable given your concerns
Please ask if you need further details