I don't think the flavor from smoking would carry over during fermentation. Oaking is a known way to impart that flavor, but is distinctly different than actual smoking.
I have never smoked a mead, but I have smoked cocktails. If budget isn't an issue,you can get a mixologists smoking gun to inject your secondary vessel then cap it off. Or for a low tech method, and a light kiss of smoke, you can " wash" your secondary vessel in smoke: slosh a tiny bit of the mead all over the walls of the secondary vessel to give the smoke something to cling to,then blow smoke into the vessel,let it dissipate,then fill it; for heavier smoke, turn the secondary vessel upside down and completely full it with smoke, then turn it right side up and fill and cap it.