A sprayer can give the lightest of mists on the glass, an aplicator will wet the glass to a far greater degree.
Also; you do not need to use a danp or wet scrim to buff the glass clean, all you need is a dry scrim, though you may well use more scrim using this method (or microfibre (which is way supiriior by the way))
Once you have misted the glass you have no need whatsoever to use a damp scrim, if you are going to use a damp scrim then dispense with the sprayer as use of either will make the other redundant.
Economy of movement...time and motion...
Using an applicator and squeegee-ing off what you can will still leave the window far wetrter than it needs to be.
Spray and buff (the best option in my opinion) or damp scrim/wet scrim is the best option for leaded (unless you have invested in WFP of course)
Ian