The only way you are going to get anything done as an intergalactic bureaucracy is to make things as streamlined and efficient as possible. Otherwise your Hegemony is going to collapse under the weight of its own red tape. Therefore, it is actively in the Hegemony's best interest to leave the low-level running of a member state hands-off, and only regulate the integration points with the rest of the empire.
Think of your member state as a black box. You don't care what happens inside of the box, you just care that the interface with it does what you expect. In the case of your Hegemony you want to make sure that taxes are collected and goods are bought and sold using the standard credits currency. As long as that is true, what goes on inside the box doesn't matter to you (mostly).
What this looks like for each member state is that the local economy works almost exactly as it always has. No strict need to remove the old currencies or do anything else to shake things up. The local government will still collect taxes from it's citizens, and some of those taxes will go towards the Hegemony. All they need to do is exchange that share from Local Currency Dollars (LCD) to Hegemony Credits (HC), using some standardized rate that the Hegemony manages. The same thing happens with inter-state imports/exports. Some good or service costs X HC, and people will know what that translates to in their LCD.
If I want to import a good that costs 10 HC, and the exchange currently says that 1 HC = 10 LCD, then obviously I need 100 LCD to make that purchase. If I get paid in LCD then I would first need to exchange my currencies to HC (which may have extra costs associated).
This is really no different than the kind of currency exchanges that we have here on Planet Earth, except that we have a handful of major currencies (USD, Euro, Yen, etc.) instead of a single universal currency that everything can be mapped to.
A similar process would happen for the local government paying taxes to the Hegemony. If the government owes 1 million HC, then it would need to collect the equivalent of 10 million LCD (or whatever order of magnitude makes sense for a planet-wide tax).
The nice thing about this set up is that it makes it incredibly easy to add new member states to the Hegemony. All you need to do is figure out what the exchange rate is between HC and LCD. After that everything is pretty boilerplate. Imports get paid for in HC, exports get bought using HC, Hegemony taxes are paid in HC, and everything else is left as-is. There is a little more work for the government to perform managing things, but the average person wouldn't have too much in the way of adjustments.
This also makes it really simple to travel between member states because you always have a standard currency to fall back to. I can turn my hard earned LCDs in HCs and then use those anywhere in the intergalactic empire.
The Hegemony also gets a very strong leverage tool in being the sole decider of every exchange rate. If you need to apply pressure to a member state then even just the threat of devaluing their LCD could be enough to keep them in line. If your LCD is suddenly worth less then your entire planet is now poorer and has less spending power compared to other member states.
Favorable exchange rates could also be used as an incentive for new members. Join up early and get locked into a low rate that gives your entire economy a boost. Take too long to decide or try to play hardball and instead you could be given a higher rate that devalues your LCD and causes a planet-wide depression. Don't join at all and you won't have access to trade goods at all. A black market would still exist for any group that didn't join, but it would be inherently more dangerous and expensive and less reliable than the legal route. And the more pieces you add to your empire, the more incentive the next guy has to join up as well.