How can I set a default tax rate that is not attached to a country?
We do not collect any address details within Magento, but we need to apply tax.
Is there a way to apply tax without relating it to a country?
Out of the box Magento requires a specific country to add a new tax rate or fixed product tax. If you're not calculating sales tax based on the shipping or billing address, you could set Tax Calculation Based On to Shipping Origin under System > Configuration > Tax. This will use your shipping origin specified under System > Configuration > Shipping Settings.
From there, you could set up a wildcard tax rate for any country you'd like. Just make sure you set the country as your shipping origin. Lastly, assign the new rate to a tax rule. You'll now collect sales tax for every order since it's based on your shipping origin.