Hello Davit
with the help of HTML mashup it is possible to put such a link. but it would appear as a new tab and not the place which you depicted but in Object Details of C4C. I hope it works for you.
with the help of URL mashup it is possible to put the link (again not button) which opens a new browser window and opens up the new mashup UI.
you can build the new mashup UI using any technology including HCP as long as it can open up in browse you can mash it up in C4C using above techniques. When you think of other technology for developing the mashup you should also think of SSO. HCP provides this capability so anything developed using HCP allow user to seamlessly navigate from C4C to mashup.
I would like to suggest you to check the different mashup capability of C4C in help.sap.com
thanks
Prabhat