When you use mullvad you create a sixteen digit id. You don’t tie an account or email to it, just your secret code.
If I wanted to answer your question I’d make an account, put five bucks on it using whatever means are functional and quick (a credit card or something) and see how it works. Mullvad is €5 no matter how many months you buy in advance so it’s not a huge deal or commitment to find out.
Once you’ve bought a month using the least privacy respecting (this is debatable) method you can figure out if it will work for you.
You may find out that you need to use mullvads encrypted dns service and/or their browser proxy setup. Using the encrypted DNS doesn’t require the use of mullvads vpn servers so you might be able to resolve the isp blocking tor that way without needing to buy mullvad.
If you find out in that month that everything is working right, re-up another month in your low privacy way then make a new account and select the use cash option. They’ll give you a code to write down. Send a big bill with that use cash code to Switzerland and in a few weeks you’ll have relatively private vpn access.
E: since the barrier to entry of €5 and some way to transfer it might be too high, you can also try to contact mullvads servers. Make an account and don’t fund it, but create a device profile and a configuration (or install their software). If your error is that the account isn’t funded as opposed to that the servers are unreachable then you’re probably fine.