A photo would be worth its weight in frakincense. As you've said, you should be able to turn off both valves to buy yourself some time - presuming you're happy for that rad to be out of action while the guests are visiting. Then you'll just lose the water in the short run of pipe from the iso valve to the rad balance valve.
OK. Not leaking from the nut on the rad side...it's the screw that controls the isolating valve that's leaking. Turning it to off slightly minimises the flow. Flow being a better word than drip.