I use this cable successfully with the D7100, since the D7200 is largely identical in construction.
I'm sure it will work as well.

I have the D7000 and it works.

On the official Nikon website, the Nikon D7200 states under the technical data: "Accessory connection:... ..., Cable release:MC-DC2....". So it should be compatible.

Shouldn't be a problem.