Personally I use a sill cloth to dothe mucky work then only detail with the scrim!!!
eg:-
soap window with me mop,
sill cloth (microfiber tesco own 2 for £2 ish)
wipe the gasket and frame all in one wipe, (yep tradman cleans frames too)
leave a 10mm boarder/wipe mark on glass
blade off window with slight dog ear on the channel,
slight detail with scrim if required,
wipe sill with sill cloth then moove on to next one
sometimes only 1 or 2 scrims a day
Good luck fella!.