I have two 6" filler pullouts flanking my cooktop. If it's a filler pullout, then unless you have large bottles of oil, I think a 6" will be fine. Note that mine are filler pullouts, not cabinets.
Filler pullouts have more space than cabinets b/c they don't have walls - they attach to the cabinets on either side.
However, if you have a range, not a cooktop, then you will probably have to use a cabinet. I don't know if a 6" cabinet will have enough room - measure your bottles and then check with your KD about what the usable shelf width is in the cabinet pullout.
The usable shelf width of my filler pullouts is 4.75" - the actual interior space b/w the "rails" on each side of the pullout shelf. So, any bottle that's 4.75" wide or less should fit.
Regardless of which you get, get one that has adjustable shelves. My KD company cheaped out on me and did not get me the one with adjustable shelves.
My filler pullouts:
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Closeup of the one on the right:
Q