Hiding shipping options for products of a shipping class

My client’s site has two shipping zones: local and UK.

For the UK zone, they offer the following shipping methods:

free shipping (over a certain amount)
first class
second class

For the local zone, they offer:

free shipping (over a certain amount)
first class
second class
local delivery

They have some products which they only want to offer for local delivery (due to size and weight) to customers in the local zone.

If a buyer tries to buy one these products and has a postcode in the local zone, they should ONLY be offered the local delivery shipping option – all other shipping options should be hidden. This shouldn’t be altered by other items being added to the basket.

Is this possible?

Thanks in advance.