Other than the aesthetic, I sincerely doubt you would ever be able to tell the difference, wet or dry, tread design wise with relationship as to which way around you mount it. If the rubber compound varies across the width of the tire there might be a slight issue. With regular Hankook automotive tires at the price they sell for I seriously doubt that they went to the expense of varying the rubber compound across the tire. The siping looks about the same on either side edge blocks so I think you are good to go there too.
According to Hankook, if they are Synergy PT or ST tires, then they have a 30 day return period. Both of these tire specifications stress the center of the tire is the reinforced section, not either outer section. However, both tires emphasize that these tires have about 110% stiffer sidewalls than most tires to ensure a squarer and hence larger contact patch. The stiffer sidewalls may not make them as suitable as other brands of tires for the Spyder. It seems the sidewall sipes in conjunction with the deeper outside channels are what contributes to their wet weather performance so from looking at them I don't think direction matters too much.
So, from Hankook's data for the Synergy PT or ST tires tread asymmetry will not matter very much, nor will tread direction, however sidewall stiffness might be a contributing issue for making them less suitable for a Spyder than other brands. Of the PT and ST models, the ST would seem to be the most suitable for the Spyder as they are for lighter vehicles and are stickier rubber from the mileage warrant duration.
You might want to try them out for a few days to see if any of this matters enough to feel, and if it does, return them. If all is well report back so everyone knows this is a serious option.