As you know the AF-I and AF-S 300/2.8, 200-400/4 and 200/2 lenses all have the same diameter (124mm) and the same attachment size for hoods. So in theory any of the hoods for this group (HK-19, HK-22, HK-26, HK-30, HK-31) can fit any lens in shooting position. Whether they are usable is another question - it's possible some of the longer options may be too long for the 200/2 VR and cause vignetting, and others may not be reversible on some lenses depending on the shape of the hood and lens.
I don't have much info on these hoods - these lenses are well out of my league and I've never handled them. I keep a list of hood specifications (which may eventually turn into a web page on my site), and I just happen to have dimensions for the hood in question: HK-26 is 125mm diameter and 130mm long. Not sure if the diameter is the inner or outer dimension? Maybe you could measure your 300 VR I and figure out if the HK-26 will fit.
By the way, if anyone has dimensions for this and any other hood, please forward them to me.