could i store the nappies in under buggy basket to save on putting in suitcase

The buggy has to be folded on the plane so you won't be able to fit anything into the basket.
You can buy nappies when you get there, just keep a few for your journey.
Ask if your hotel will provide a cot for you. Or you might be able to hire a travel cot from a local agent when you get there.

Take a baby changing bag - it doesn't count towards your hold or hand luggage allowance and holds enough nappies for a few days.

Compact travel cots are available, ours weighs less than 2kg. Alternatively the accommodation provider can usually get one for you.