For the price of the kit and the hassle of trying to do it, something that small, I would just send in. Probably cost the same and be professionally done.

Allen,

I'm guessing that the original finish on these knobs was chrome. Nickel would have been too expensive, if modern economics hasn't changed from the 1950s. Zinc, I just don't know, all I can think of is screws from Home Depot, so I'll stick with chrome. Before you go to the expense of plating those knobs, have you tried some of the big bingo parts sellers? There is Joe Shope, who once told me he bought out the inventory of four different operators. I've bought a few bits from him over the years. You can find Joe with a google search. There also are a few sellers on eBay who appear to be operators clearing out their old stock. One guy from Seward, PA seems to have a lot of game parts. I can dig around and come up with his eBay name if you want to try him. As far as refreshing the red arrows, I'd get a bottle of hooker-red nail polish and fill in the engraved designs. You can remove the excess with alcohol after the polish has dried and it will look great. I think I did this once on one of my games.

"Big Time" was made in 1954; don't know wht metal they used. Nick probably knows.
My "Big Time" also has formica on it, but I'm okay with it.

I don't, unfortunately. I'm definitely not a materials expert (but thanks for the confidence).

I have always heard/imagined that the 'shiny' metal on older games was nickel and then eventually stainless (depending on shape). Zinc would be for things that you don't touch (coin mechanism receiver). I don't know if chrome plating was actually used or not, but it would be interchangeable with nickel. If it was cheaper to use chrome (and I imagine it would be), then I definitely think BCB's advice makes sense. The nail polish idea would work well. Enamel paint is what will look best. And it's really easy to do - slather on, wipe off. Nail polish would also work well, again as BCB suggests.

If you intend to do your own plating, I would suggest that the control knobs themselves might not be the place to start. Any flat portion is ok, but the ridged areas will be a nightmare using the plating kits (in my opinion). Also, with those kits, prep to an insane degree - sand the area to be plated until the area is feathered into the remaining plating. Clean it well and then try to plate. The plating can take a few 'coats' to build up to where you want it to be.

Good luck, share the results.

Allen, once you get it figured out you'll need to swing by my place again and give me a lesson.

Allen, chrome is the right choice IMO. Chrome has a slightly different look than nickel so in some circumstances that would be a matter of preference. To my eye, chrome has a grey cast whereas nickel has a silver/white cast. You should familiarize yourself with the look of each to see if you prefer one over the other - you might. Chrome is very hard and will be much more durable than nickel. But if you should absolutely dig the look of nickel you could still do nickel with a clear powder coat. It would still take awhile to wear that out.
The parts to be replated will have to be stripped of their existing plating. And plating - like automotive paint - hides nothing and will only be as good as the surface preparation underneath. Good luck. I think it will be worthwhile.