Question about machining firing pin hole

Hi ! I'm converting a Uberti black powder revolver to .45 Colt. It's the exact same frame as the Cimmaron new sherriff, and takes all of its parts, so I ordered a new cylinder, barrel, and firing pin in .45 Colt. I've already fitted the barrel and cylinder, with zero end play, front sight at 12 O'clock, and a .004" gap between cylinder and barrel, and the last job is the firing pin hole. It's a different configuration from the black powder pin, so I tig welded the hole shut, and I am ready to machine out a hole for the centerfire firing pin. It is essentially the normal tapered arrangement you would see on an older revolver (without a transfer bar), and so I want to make a tapered hole to "funnel" the firing pin into battery when the hammer drops. What do you think would be the best tool for drilling this tapered hole? Maybe a center drill just over the pin's tip size with a countersink?

Sounds good to me.