Well... There is Tiber's face on the coins, and were named after Tiber, so yeah they will stick with them. Besides if Dunmer can still use them, Nords could also.
If none of the holds have the resources, specialists, or equipment to consistently mint coinage to the standards of the the septim--whether those standards are metal content or consistent weight or magic mint marks--then it makes some sense to keep using such an established, widely-circulating, and reliable currency, even if it originates with the enemy and has undesirable symbolism.