No, they not only don't have the manual dexterity they'd simply turn it upside down and waste it. They also don't have the cognitive ability to do more than see the cup and try to manipulate it to their mouths. At this age they're doing well to hold a bottle.
Find a tippy/sippy cup that you can stand and use them. Buy a dozen of them. We found we liked the ones with the oval insert instead of the ones that had the long narrow insert.
The oval ones were much easier to clean inside, a Q-Tip did wonders and we always soaked them in mild bleach water before washing them.
So no, you're going to waste all your breast milk while your thirsty baby finger paints and plays in it.
I would not transition that baby to a bottle, no way.
AND before there were bottles the mom's breastfed until baby was weaned and that was much older than 10 months. If the mom couldn't make milk there was usually some other woman in the area that would take on feeding the baby and helping out. Or the mom made a bottle from a glass bottle and put a finger from a glove or something over the end of it.
Here is a link to show that there WERE baby bottles in early history. The one is the picture could be from the 1300's BCE, that's the OTHER side of the zero that marks common era, or AD.
http://en.wikipedia.org/wiki/Baby_bottle
But I got it, that you want to take your little infant and hand them of cup of your breast milk and then hold it to their mouth and suck it in and not spill it or tip it over.
That's not a likely scenario. I understand you have to go back to work but please, have some compassion for your care giver. They are not going to want to spend the day cleaning up spilled milk then not having anything to give to your child to eat. Your baby needs to be using a tippy cup now so she can get used to it without the stress of mom leaving her with someone else.