Adding shielding to existing cables

So I have some interconnects that are picking up all sorts of RFi. I know this for two reasons, one, as I move them around the noisy/buzz sound changes, and two, when I switch them out for shielded interconnects the noise goes away.

so, I bought some tinned copper shielding and some new RCA plugs. I’m going to cut the existing RCA plugs off the existing cable and install the new shielding and new plugs. The thing is the new plugs have a plastic body so there is nowhere to easily connect the shielding to ground.

I was thinking of running a pigtail from the shielding and attachIng an eyelet to ground it to my preamp since there is a grounding lug. Would this work or is there a better way given what I intend to use?