Will the electrics cope with everything running at once?

They will if the supply is calculated properly rather than assumed. Two dryers, straighteners, climate control and lighting running together will defeat an undersized circuit. We work out the total load, run a suitably rated cable from the main house, and place a socket at each of your styling stations at working height rather than at skirting level, so nothing trails across the floor. Every workstation gets what it needs, and the whole installation is certified under Part P.