I would ring up BA and see if they can provide a full JFK-LSI routing via EDI or GLA. It may or may not show on BA.com but a chat with a knowledgeable agent should see if the right price is showing.

If booked as a BA codeshare, so a Loganair flight marketed as BAnnnn it will get TPs, Avios and eligible flights. If eligible, also lounge access in EDI or GLA. To get a codeshare you need at least the LGW or LHR sector on BA. I regularly do flights of this sort and there's no problem, you can check in for the Loganair flight on BA.com and get your boarding pass online from there.

The JFK-LGW service is new so we can't be sure of the reliability yet. With an ontime arrival then the connection is perfectly possible, I've gone from international arrivals to departures in under 20 minutes, admittedly when the passport queue was swift. Two hours strikes me as a good turnaround for LGW, but if booked as one ticket, indicated in my first paragraph, then your connection is protected, BA will get the passenger to Lerwick if there was a problem such as a late arrival. I would avoid going via LHR if you can, looking at a GLA routing if necessary.

So I would call up, and even if was more expensive this way, I would pay for the single booking, within reason: you are getting something for that extra cost. If you don't do this, then you take the risk rather than the airline.