For those who want a disposable alternative, Personna Carpet Trimmer blades fit in a standard utility knife, and are edged like a grafting knife.

http://www.amazon.com/Personna-Carpet-Trimmer-Blades-Wrapped/dp/B00GU2ZMYG/

Once you are well aware of the basics, the  dexterity  with which the grafting (or budding)  is done, depends mainly on the type of knife and how sharp it is.
A strong, sharp, carbon steel grafting knife with, say.. 2 1/2 " blade is well adequate. It could do dozens of grafts before re-sharpening.

Francisco
Portugal

Can anyone recommend some sharpening stone grits for grafting knives? I have a few knives that are rarely dull. The video on this page doesn't mention specifically any grits.

See these two economical stone combination options for a start.
If you have no previous experience with sharpening stones I would suggest the 120/1000 model and see how they perform for you.. As you gain practice you may add one or two additional types/grains  if you need.

http://www.sharpeningsupplies.com/Naniwa-Economical-Combination-Waterstone--P559.aspx

If you have to do a lot of grafting/budding I would advise hard carbon steel blades instead of stainless.

Francisco
Portugal