Do I need to shorten chain when fitting a new smaller cassette?

You can try it since it will not cost you any time or money to try it other than swapping the cassette and putting the wheel back on.

You might just be able to get away with adjusting the B screw slightly.

Here is a link to sizing a chain.

https://wickwerks.com/setup-chain-length/

As the smallest cog and smallest chainring have not change changed size, the chain length will be no worse than it was previously. With the smaller large cassette cog, you may find you can shorten the chain, giving better small/small tension. The difference (presuming a reasonably sized chain to begin with) of dropping a link will be minor enough I doubt I would bother.

However, as pointed out in comments by @Craggie - when fitting a new cassette, its usually false economy not to fit a new chain. In that case, make the new chain the best size for the new cassette.