The best thing to do is to install the new chain, and then see how your bike rides. If you get a lot of skipping in your favorite sprockets, then it is time for a new cassette or freewheel.

The occasional skip may work itself out over time. That is up to you, but it may be a sign of looking for more replacement parts for the next time you replace your chain.

The shop likely will replace a cassette or freewheel if there is any question about reliability. Easier to charge a customer $100 than to have them angry for only doing a half a job.

You can likely find cheaper parts if you hunt.