rpiano,
This recipe is more of a Beer made with honey as there is ever so slightly more fermentables provided by malt than honey, but it is so close it can be called a braggot for all intents and purposes. Since it is a beer, the answer to the cucumber smell may be found in John Palmer's list of off flavors/smells in his "How to Brew" book. Check
here and see if the description of any of the off smells matches what you are sensing. From the recipe, I am assuming you made this the same way you make your beer (boiling the wort, rapid cooling, aeration, pitching etc). Did you boil the honey with the malts, or add it in the fermenter after cooling?
Since this smell seems to be appearing in all four Meads (or are the other 3 batches also Beers with honey?) you have made so far using this honey, the cause may be a component of the honey. To test this, dilute some of the honey down with distilled water and see if you can detect the same smell (get some friends to help with this in case you cannot detect it but others can). How old is the honey? Has it crystalized with more liquidy honey on top? If so, there could be some bacteria living in this upper part that could be affecting the flavor. Has the honey darkened over time or is it still a nice light color?
If the honey is not the cause, you will have to look at other options. For example, it may be that your equipment has some scratches that could be harboring some nasties (plastic bucket used as fermenter?); the hops you are using could have oxidized a little; or simply that the Mead is still very young and needs more time bulk aging to allow the specific component you are smelling to dissipate (acetaldehyde can create a pumpkin smell, which you could be perceiving as cucumber).
Hopefully, you can dig down to what is causing this flavor. Provide more details as to your process, storage methods, ingredients etc. and perhaps we can spot something that you missed. Let us know how the honey tasting goes, and do contact the apiarist who may know exactly why the honey tastes the way it does.
Angus