Would it be useful to research the flow rate of a typical pressure washer so you would know how quick that time was and can plan your water supply accordingly?
It would also be useful to compare the delivery pressure of the cordless machines with main-powered ones.
Six litres a minute is typical for a Karcher K2 size machine, so a 25 litre drum (far more easily transportable than a bucket as the drum has a lid) gives you 4 minutes of constant washing. With two drums and a lackey named Aquarius, you could wash continuously.
Bosch make a couple of cordless machines (note that the flow rate for the B&Q one [2.17 litres per hour] has to be incorrect). The one offered via SF has a flow rate 1/3 of the Karcher.
https://www.diy.com/departments/bos...less-36v-pressure-washer/4059952582344_BQ.prd
https://www.screwfix.com/p/bosch-fo...x-2-5ah-li-ion-cordless-pressure-washer/620HY
Is a second hand (Honda) petrol-engined one a possible option? Drain the tank at the end of the season and run it for a minute on Aspen fuel and it will start first go in the spring and last forever.