Old Fashioned way for me.
Caulk it, Lead it, Putty n paint to finish for me personally.
You'll enjoy yourself!
Use original style Cast Iron with ears and fix it using 6" Spout nails and Bobbins.
It's an old skill that should never be allowed to die and this is your opportunity to keep it alive.
For a real old fashioned authentic job you could do it off a rickety old wooden ladder. Take the existing ones down with trembling knees, sweat on your brow and spiders climbing about on you. Then use a raking out chisel and wooden wedges to fix the new one back.
However, this is 2018 and that is no longer allowed as you know.
When you're doing it though, give a minute to think of the old timers who worked with that stuff all day everyday, off a rickety old wooden ladder.