The magazine from my oxygen supplier (Baywater Healthcare) has the following article :-
'You must not use e-cigarettes whilst using oxygen.
These devices contain a battery and electrical components, including a heating element to vaporise liquid. The vaporised liquid is usually glycol or glycerine based.
These are electronic devices with potential for spark if a fault develops, and they vaporise a potential fuel source. y
You must not use them whilst using oxygen.'