Would adding CNAME records in DNS server for setting up DKIM cause email server issues?

The DKIM signatures are checked against DKIM DNS records, but not the other way around. As the selector could be anything, without a signature stating the selector there's no way to even tell whether a domain uses DKIM signatures or not. There's simply no way to know where to look.

That's also exactly why Microsoft requires you to have those CNAME records and performs the checks before they start DKIM signing any mail.

Well, there's one conflicting condition: if you are already using the same selector for DKIM signing with another service provider, adding a CNAME that replaces that selector would possibly interrupt their services, resulting in signatures that couldn't be verified. That's unlikely, but possible.