+ 1 to Box Knife or Folding Utility Knife.
Both are cheap, cheap, cheap, and can be replaced easily if lost or broken.

Both can be sharpened, exactly the same as sharpening a knife. Get a stone or sandpaper attached to a flat, and alternate strokes on each side, as if cutting a slice off it.

I would submit that it is far more effective to buy blades. Bingley made several great points. To expand:

1) depth- A box knife set correctly will be a very shallow cut, which is a very good thing.
A) Less risk to the package
B) Less risk to you while cutting
C) Less risk to you if dropped, or picking back up. Kitchen knives have a longer exposed blade, when setting down and picking up (assuming more than one box) you have more risk.

2) sharp. I think we all agree that sharp is better; less effort to cut, cleaner cuts, less damage to you if, god forbid, you cut yourself.
You can totally sharpen a utility blade. It is NOT best practice. Replacing a blade on a well designed box/utility is fast, and easy. Sharpening a blade that is covered in GLUE is not. Since a MILWAUKEE 48-22-1901 FASTBACK FLIP OPEN UTILITY KNIFE (not a sponsor, nor selling, just an example) is about 10.00$, and 100 replacement blades are around 12.00, and each blade has 2 sides, you have 200 cutting surfaces that are literally razor sharp for ~ 22.00