Is there any way to set cookie to all the sub-domains of a domain (Domain=.site.com) but exclude just 1 domain?

We're in a situation where we're pointing one of our sub-domain (sub.site1.com) to a third party application (app.site2.com) through a CNAME record. I don't want to send user cookies to their servers. Is there any way to set cookies to all our sub-domains except for sub.site1.com? Please help.

I've tried different variations of Set-Cookie with Domain specification.