What do you mean by 'remove the enchantment'? Like, remove it permanently off of the pickaxe, or remove it, but also give the token of the enchantment you just cleared to your inventory?
If the first option is what you meant, then I don't feel it would really be worth it. It's better having enchantments, and explosive actually helps mining.
Otherwise, well, as you said you would need to pay the cost for the enchant removal. It would end up in your inventory as a seperate item that you could drag onto another pickaxe, or sell it, perhaps.