If I recall correctly, 39N you shouldn't have an issue staying IFR. 47N however, at least when I was flying out that way 2 years ago, didn't have an approach or DP that could get you in or out of the airport without entering the 10NM ring since they were all pretty much entirely reliant on SBJ VOR for the departure, approach and/or missed and the 10NM ring was so close on the west-side of the airport that an overshooting turn from base to final would put you in the TFR.
I know there was a lot of talk about the FAA doing something to fix it to make 47N more accessible, especially since Trump's summer trips to Bedminster shut down Solberg and Somerset for weeks at a time making flying in the area a royal pain and interfering with planned events such as Solberg's annual balloon festival. Looking at the procedures now, it looks like they changed the DP to use Yardley (ARD) and I think they modified the GPS approaches; you're still SOL though if you are in actual IMC and arent a /G (or rather the ICAO equivalent) since the VOR approach still uses SBJ.
There's no issue cancelling IFR in the air and finishing VFR though. In fact as illustrated by the 47N, it might even be necessary if you aren't a /G. I do however recommend staying IFR for as long as possible going into the TFR which means if flying into a towered airport, finishing the flight IFR and letting tower close your flight plan for you.
With a non-towered airport, I'd wait until I have a good solid visual on the field and ATC is telling me to change to CTAF. ATC is pretty good about reminding you to keep your squawk code until you're on the ground but still remember not to change it out of habit and to reject the instruction if ATC accidentally tells you to squawk 1200; I doubt that close to the airport TSA, Secret Service and the military would make a big deal of it if you did accidentally switch but as others have noted, the FAA will still take any sort of non-compliance like that very seriously so they might try to violate your ticket.
Getting out of the TFR, I'd say just file how you are going to file (VFR or IFR). Except for your specific departure instructions, the radio-contact procedure will be the same regardless of IFR vs VFR or towered vs non-towered. No sense filing IFR if the entirety of the flight after clearing the TFR is going to be VFR and ATC will tell you when you are clear and able to squawk 1200.