Which version of ServiceDesk are you using and are you wanting this via Console or WebDesk or both?
There is a Desktop Manager module connector called "External Connections" (licensed so you may or not see depending on whether you have DTM in the first place and then the relevant connector) which allows you to fire an external exe and pass it parameters so launching VNC viewer and passing the host name from a field in LDSD would be a possible solution.
Yes I want to run both console and webdesk. I'm currently using 7.8.2
Yes in your version DTM supports this in both console and Web Desk