It's hard without knowing more details, but there's potentially more at stake here than just conforming to 'best practice' for hiding or disabling options. The most important thing is that the user is able to make informed progress throughout checkout.
It's unclear whether you're expecting users to use the checkbox or the dropdown first, or if they are available at the same time which is leading to this conflict. It should be an ordered but easily correctable flow.
Consider the two possible order of events:
1) Choose payment option with checkbox, then delivery option via drop down.
This seems wrong. People choose a payment option once they know the final price. An expedited option may mean the user doesn't have enough points or doesn't want to use their credit card.
Shipping method can make or break a deal. If I can't get expedited delivery for this weekend, I'm not interested. If I had chosen a payment method first and then been denied the option to choose a delivery option (perhaps one I had previously used) then I might abandon.
2) Choose delivery option, then the payment method
This is the usual method. You add stuff to your basket, choose a delivery method, add coupons, etc, and finally select a payment type when you have a total, and immediately prior to enter actual payment details.
Here, the user still has all the delivery options. The user may still be expecting to pay by credit card, so silently or invisibly rejecting a payment option in the next step may confuse the user, so they should be made aware at the point of choosing delivery method.
If some delivery options mean that the credit card option wouldn't be possible then you want to indicate that up front. Then there should be no surprises when it comes to the payment option.
One way to do that is to default to the delivery option which enables both (or all) payment options - giving the user the most choice. Then when (if) the user changes to a delivery option that disables/hides a shipping option, the user will see the payment options change. The user can then switch delivery option back again if they want to - because they saw the impact.
As an example, XCart do something very similar - In the example below, the user initially sees options for 'pick up in store' or via 'courier'. The default 'in store' option means cash and card payment options are available. If the user changes to courier option, then (in this case) only the cash option is available.
You could still indicate discretely to the user that they can 'Change delivery option for more payment methods'