The plus side of this coating shows the attention to quality and durability of the original manufacturing process. Handling the linkages (rather than say wire brush cleaning them) should be safe, but of course wash hands afterwards. See
http://www.poeton.co.uk/w1/cadmium-plating.htm below. So, I wouldn't be afraid of it, but the job might be a bit challenging mechanically if you only have a screwdriver. If you have the budget you could get this job done in the UK (you should just post the motor unit), if not it would be nice to have a mechanically confident friend with you to help.
Otherwise, just take it slowly buying good quality tools as you need them. Just working on it at weekends is fine.
By the way you have a nice SME 3009 Improved tonearm there. The fact that the headshell is not removable means that you should definitely remove the stylus of your cartridge before trying to remove the motor unit from the chassis. The leads to the tonearm are easily unplugged.