There should be no problem with using these spells in combination with an Artificer’s Thunder Gauntlets.
The gauntlets count as weapons for the Artificer, and it should be obvious that a pair of armored gauntlets is worth some amount of money, whatever that amount is, so it ought to meet the requirement even if we don’t know what the actual value is.
The purpose of adding the 1 silver piece cost to the weapon component of booming blade and greenflame blade was to fix a weird exploit related to component pouches.
A component pouch “hold(s) all the material components and other special items you need to cast your spells, except for those components that have a specific cost.” Since booming blade and greenflame blade had “a melee weapon” listed as a material component, but didn’t list a specific cost, in theory this allowed a caster to just produce any melee weapon out of their component pouch in order to cast the spell, which then I suppose just vanishes back into the ether (or worse, just hangs around, existing).
This is absurd and obviously not the intent of the spell, but to fix the exploit, the devs added an explicit cost to the weapon material component, which happens to be equal to the cost of the cheapest melee weapon in the PHB.
In theory this does exclude weapons that do not have an explicit value, but since that wasn’t the purpose or intent behind the update, it really shouldn’t be a limitation on the players. As long as you have an actual object that counts as a weapon, you should be able to use it to cast these spells.