If you wanted to replace the foot control with another vintage one, buy a carbon pile type....no wire coil inside. Or if you wanted a new one, you could buy a carbon pile or electronic control.
Actually I just bought a "new, old stock" Kenmore carbon pile control on ebay for $9.99...part # 6802. It's the same one that came with the Kenmore I got new in 1971....Bakelite housing, metal bottom. I was really happy to get it...It's the best, most responsive control I've ever used & I've been sewing for over 50 years! I've bought several of this same foot control on ebay before (used but VG condition) & rewired for some of my other machines. But I was thrilled to find a brand new one!
And I also have never heard of grounding a sewing machine.