So, the 2 small wheels were on the back and the 2 big wheels on the front?
Then why trying to pull off the wheels, instead of just removing the axles from their holders - with the wheels still on - and putting them in the right place?!

These waggons came with the wheels already attached to the axles. Swapping the front and aft axle should be no problem, normally the axle-holders won't break or something if you handle it with some care ...
If the holders loosen too much so the axles might drop out, add some small bits of thin invisible tape around the axle in the right place and voilĂ .