I would suggest giving him in a different bottle. In this way, he can differentiate when drinking milk and drinking water. Using the same milk bottle, he would have to lie down or raise his head to drink water. Using a sippy cup or a drinking bottle,he can drink when he's sitting upright. I used this bottle (as in pic) when he started solids. I bought this at a shop call SUNDAY 2000.
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It is up to personal preference. For me, I will use different bottles as the bottle that baby is using for will have smell of the milk.
If the bottle is thoroughly clean and free from any residue, I don't see why not. If not, consider sippy cups?
I think it's totally fine!