Changing a plug ona soldering iron

[Guybrush]

Hey hey

I have a soldering iron (This one: http://www.banzaimusic.com/Soldering-Iron-LKR-50.html) with a 2 pin European plug.  I was wondering if it would be safe to replace it with a UK 3 pin plug?  Through the clear casing of the iron I can see that the flex contains a live, neutral and earth wire.  I'm confident in physically changing it but not sure if I'm going to fry a component/myself in doing so.

If it helps the fitted Euro plug 16A 250V.

Thanks in advance!

EDIT: I should mention that I have Googled this and it looks like it will be ok to change the plug.  I just wanted to double check with the knowledgeable people on here and thought it might one day help someone else who has the same issue.