You can do assessing part time if you want to.
I did it full time but there were colleagues who just worked a few days in the week and worked elsewhere the rest of the week.
As far as training to be an assessor goes a lot of training providers do training on the job and will pay for it for you. You're best contacting your local training providers and colleges to see if they do dental nursing and enquire about any positions they may have.
You are paid a wage as you complete the training but you will probably find that your wages are increased once you gain you assessing qualification.
Hope this helps