Will credit score drop after replacing credit cards?

You should note that cancelling a credit card won't help your credit score. In fact, it may actually hurt your score and can reduce it by some points.

Card replacement will not hurt your score. You are not cancelling but simply replacing them.

Creditors will cancel the old account number, and issue you a new card, retaining the significant dates of the account itself.
Closing an account, even if that is how they did it (and they wont) is not actually as detrimental to a credit score as some believe. All you immediately lose is the CL on the account, which could affect your overall % util. Closed and open accounts both count in the calculation of your average age of accounts, so there would be no impact there. Closed accounts normally remain in your credit file for up to ten years after the date of closing, so you would have ten years before that could impact your credit score.
If they reissue the card with its prior CL, there would be no adverse credit scoring impact.
Just make sure that when the account is reported, the original date the account was opened is retained.