Why not to have a link to the contact search in LinkedIn, populated with the contact name from HUbSpot. (similar to the one that takes me to a corporate website). I know you have issue with pulling information from LinkedIn - no issue there, but a link to the search with contact name inserted would be a nice timesaver.
Currently it is a cut and paste process from HubSpot, vs a single click (as with Insightly for instance). There should be no legal issue with that - just save a cut/paste effort.