Is there a reason he only nurses 3-4 times a day????
For the 1st year of life, per our Pediatrician, a baby should be fed on-demand 24/7 for the 1st year.... it is a baby's primary source of nutrition.. .NOT solids and NOT other liquids.
If nursing, nurse BEFORE solids. Otherwise baby will be too full to nurse, and then it will cause a baby to "wean" from breast.
Next, how is your milk production? The more you nurse, the more your body will produce milk....it is the body's way to KEEP UP WITH the needs of the baby and their growth-spurts. So that they get adequate intake, daily.
I would not give him a lot of water. His liquids should be from breastmilk. Direct nursing is best.
At that age, my kids as babies were still nursing about every 3 hours. More if having growth-spurts. Sure, they were on solids by then, but it was not their "main" intake. Breastfeeding was.
I would offer him a bottle, for breastmilk, since he is not taking a sippy cup for it. Babies OFTEN do this... it has a "nipple"... they associate a bottle with the breast. Many babies will NOT drink "milk" or breastmilk from a sippy. For now.
You can always teach him about the sippy later. Not now... because you have a time deadline.
You said he refuses the bottle... because he does not like the Similac... can't you try another Formula brand??? I would do so now, before it is too late. It will be trial and error.
Also, pump a ton of breastmilk for him before you leave. Freeze it.
I would have him nurse more often. Only 3-4 times a day is NOT much.
all the best,
Susan