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. Iā€™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?