Put his bottles out, where he is, on a table.
Via getting use to seeing it out and about, he may learn... to just grab it himself and self-drink.
When my kids were babies, I did not only offer them water/milk only when "I" held it.
I kept their sippy cup out on the coffee table, around them. That way, they got used too seeing it, knowing it is theirs and that you drink from it/grab it/put it to their mouth, themselves.
And whenever thirsty, "they" could grab their bottle or sippy, themselves.
Thereby promoting self-direction.
I let my kids drink water whenever.
I left their sippy of water near them anytime all the time, on any low table where they were. I would say "here is your water/milk..." and then told them they can drink when they need to.
This teaches them, self-reliance as well.
And knowing how to do it.
I did NOT, when this age or 1 years old or after, hold them or it, for them.
They easily just grabbed their bottle or sippy cup, themselves.
NO problem.
I did NOT only give them liquids, at meal times.
It was, all the time.
Kids need to learn how to self-regulate too, their thirst. AND to know, their body's 'cues' for being thirsty and then, drinking, from their cup or bottle or whatever.
Kids... need to drink, on-demand. Meaning, if they are thirsty and need water, they can do so and drink.
Not ONLY at meal times.
I myself for example, do not drink water or liquids ONLY at meal times. I drink, all day.
Kids need to, too.
Don't only limit his liquid intake or drinking, to meal times.
A kid, as they get older and active, need to drink, when they need to or are thirsty.