Hello and welcome to GoY.
I moved a skimmia in October last year which had been in the garden about 8 years and it's done OK. I moved it as it was overshadowed by other things and put it into a more open location.

the best time to attempt such a move would have been autumn last year. If you do want to try, bear in mind you will need to keep the plant very well watered from some weeks until it has settled in, especially at this time of year. If you live anywhere that's going to have a hosepipe ban, this might not be possible.
If you want to try anyway, keep the largest rootball possible round the plant, and reduce the topgrowth by a third to give it more chance.

Depends on where you are moving it to and the soil conditions ... Skimmia Japonica prefers a well-drained neutral to acidic soil, and flourishes in partial shade.