Good day Okido,
The fact that the cream is low risk combined with the fact that operator's hands do not touch the food contact element of your packaging makes the risk of any contamination very small. What packaging do you manufacture Okido is it plastic containers / cups?
From what you have told me I would be very confident in saying that you are OK with the hand cream system you have implemented.
There was quite clearly a need for hand cream in your facility, that's why people brought their own in. You have addressed a potential problem sensibly and instead of banning its use you have provided a central source that you can control. No excuses for Operators.
Except that is until you find that one or two Operators are still bringing their own in because they don't like the hand cream that you have provided - 'it doesn't suit my skin.' Just some personal experience of mine and in the end we had to have two types of skin cream.
Good Practice Tip:Make sure the cream dispenser has a label affixed to it with the ingredients list, safety data etc. That goes for soaps too.
Regards,
Simon