There are a number of sources, including the Virginia Camellia Society, that recommend propagation from softwood cuttings taken from April/May (after flowering) onward.

I thought most recommend doing cuttings in late summer after new growth has hardened, but I've never tried earlier. So you do last season's growth then?

That said, I'm trying to graft this spring. We'll see if it even works. I had success with a fall graft.

https://www.americancamellias.com/care-culture-resources/propagation/rooting-camellias

We made our Camellia sasanqua cuttings in Autumn, at the time of flowering. Just snap off the flower buds.

Hartmann-Kester say:

Cuttings are best taken from midsummer to mid-fall from the flush of growth after the wood has matured somewhat and changed from green to light brown in color. Tip cuttings are used, 3 to 6 in long, with two or three terminal leaves. Rooting is much improved if the cuttings are treated with IBA quick-dips of 3,000 to 5,000 ppm, 6,000 to 8,000 ppm IBA plus 2,500 ppm NAA, or 3,000 to 8,000 ppm IBA talc. C. reticulata hybrids root best with 8,000 to 20,000 ppm IBA talc. (Note: IBA 3000-8000 ppm is 0.3%-0.8%, so this is much higher than the talc stuff at Home Depot)

Camellias also may be started as leaf-bud cuttings which are handled as stem cuttings.

In this case, high auxin concentrations should be avoided because this may inhibit development of the single bud. (<<<<Interesting bit this)

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However, if you want to prune just go ahead and do it whenever you feel like, (because I'm an impatient gardener.) Maybe leave a few unpruned branches but strategically air-layer them where you would like to do the prune cut.