Compressed air is a little too strong it can bend the fins. Canned air works, as does a shop vac set to blow instead of suck.
You also should not have much actual dirt in your radiator on an L series. It's way back in there and you should be cleaning it like this REGULARLY.
There is almost no heat overhead available on an L series so you don't have much leeway between normal operations and an overheat condition. That gauge can go from normal temp to max in under a minute if you're working the engine, especially while mowing.
I religiously blow out the radiator every morning before operations and before I fire it up again after lunch if I'm mowing. This has kept my L series down in normal temps the entire time I've used it since my near overheat.
When I wash the tractor before I put it into storage, I run water through the radiator to keep it nice and clean. No dirt gathers in my radiator, it's vile evil stuff that I keep outta there! No mud allowed! LOL!