Hi,
Would this not depend upon what you are welding, where you are doing the welding, the position that the welder is welding at, the amperage you are using etc, etc.
I think the best place to start would be the HSE’s task specific guidance.

http://www.hse.gov.uk/welding/guidance/

Remember to consider the tungsten electrode as thoriated if I remember correctly is radioactive and is best replaced with ceriated electrodes

Thoriated electrodes are definitely radioactive so, if you use them, you need to follow the advice given, particularyl about the control of exposure to dust when grinding them.

TIG welding, on certain alloys, produces significant quantities of ozone. You also have to consider the shielding gas, which will probably be an asphyxiant (look at the data sheets). The amount of metal fume produced by TIG welding is relatively small, but the health risk is not insignificant if you are welding the more toxic substances, such as nickel.

No-one can supply an effective COSHH risk assessment for your process without knowing what you are welding, and more about the process parameters. The advice already given is very good.