Need some advice. I want to run some software on my work computer, but it's an independent third party software (artisteer) so I'm very wary of running it on an NHS computer. Is there a way I can run it from USB into a sandbox software which means it can't access/interfere with local software?

Could you run it on a personal computer? Though with something like Little Snitch running to see what it is sending and receiving online. That would resolve many security issues.

I don't really want to lug my laptop into work.

Set up a virtual machine, although it means you would need to install the 'player' software on the work machine. You can define that the VM doesn't have a network card, although that means you can't save the work locally or print to a network printer.

Will it run on Linux?
If so, run it from a live Linux CD or USB stick.
I carry around Linux mint in case I ever need to do something on company laptop. Yes, most software won't work, but some things can be done just as on windows.

VM is the only way on Windows. But then you'll need a Windows license as well.
I use Artisteer myself and it's well written so shouldn't effect the computer it's on.

Using unlicensed software on a company computer is normally a disciplinary, if not stackable offence.

I was assuming that the OP has the relevant licenses.

TBH this is the NHS. I'm having to downgrade IE8 to IE6 so we will be able to run choose-and-book. In theory, the PCT supplies the computers and we're responsible for anything that happens. So we could run software on it. Obviously if it destroys the hardware, it's our own fault and we need to replace it.

My only concern was whether I could install/run Artisteer so I can design the practice website at work - it makes life a lot easier when all you want to do is fiddle with the colour scheme and show the results, rather than having to do it at home and email over the website.

Dang - Windows only, I guess. I was going to suggest your practice invests a massive amount of cash in a Raspberry Pi for this.