I agree with esshup - use the paintbrush for applying your poison. Spraying is much faster and easier, but your risk of getting poison straight into your water is much higher.

Further, you may not need to cut and poison every single willow. If they are growing in clumps and bunches, then cut the easiest main trunk stem you can reach and poison at least one in every clump. You will definitely not kill them all, but then you can go in for a second pass later and kill the ones you didn't get the first time.