This is a cute project! Great idea and a cute logo to go with it.
What size chart do you have now and how big does it have to be? (Maybe you can just accept every square to be 2 stitches and 2 rows or 3 stitches and 3 rows and just work from the chart as it is).
You can always draw the chart by hand with a big print of the logo on paper and calculating how wide of a grid you have to sketch over it. But if you have a sufficient grid already it would be easier to work off of that.
The color I would match in the store with something with the exact logo colors to hold onto the yarn. Online pictures will definitely not do for an exact match.
I do not remember ever seeing color numbers of general type on yarn or yarn sites. Maybe somebody else will know something about that, though.