Ken Davy will be limited on where in Huddersfield he can build a new stadium. Planning these days will take into account access for people, usually by means of public transport, so the only place near the town centre with enough space would be the Old Gas Works, and no one has ever been in a hurry to develop that site.
Laund Hill and Huddersfield RU have both been mentioned, Can't see the RU club wanting to have someone come into their profitable operation and want a slice of the pie, and Laund Hill is a poor location.
As sentimental as a return to Fartown would be, parking and access would be a nightmare.
Final option would be the old Police Training Ground as it was known (Woodvale Park?) which again is a long way out of town, I believe Ken Davy purchased this years ago when the police disposed of it as an asset but could be wrong.
So imagine a scenario where, having confirmed they are leaving the John McGalpharm, they then say they cannot find a suitable site, so are looking at exploring the lease at The Shay, it's not impossible