Wait until early October to move to cause less stress to the shrub. you could trim it back at the same time.

The proper name of your plant is Euonymus alatus and as Moongrower says it will be better transplanted when the shrub's in its dormant state or the 'shock' that plants experience will kill it.
You'll need to take the rootball intact - and as a 4 year old shrub that'll be large - or the plant will take twice as long to re-establish.
Make sure that you prepare the new hole twice the size of the rootball and that you incorporate composted manure at the time of planting too, to give the poor plant the best chance of recovering.

Lift in the dorment period and follow the above advice, E, Alatus will grow very big in time, however keep it to the size you want by trimming slightly, this you can do early spring time.