Yes, in Pano2VR you can do that. It is possible to directly link to a panorama in a virtual tour.
If you want a virtual tour for the website with map and additional info in the panoramas this will be the ideal solution.
Not sure about 3DVista, as I do not us it.
If you just send the spherical images to t he webdesigner they will have to come up with a solution for the viewer (to display the panos). In general you can decide which way works best for you and what is more economical.
You also can outsource the tourbuilding to an expert and then hand the final tour to the webdesigner how easily can integrate this into your website.