I can think of three ways to solve your problem (of course there may be a hundred more ways :-)
My personal PayPal Account is in EUR. Each time I buy something overseas in USD (or any other currency), PayPal will directly do a currency exchange USD --> EUR (they earn money by transfer rates in this process) which means my PayPal account will be debited in EUR. So I can't think of any problem when you buy something via PayPal.
With receiving money it's similiar. Your PayPal account has a primary currency, but you can receive payments in other currencies. In that case you will be asked if you want to exchange that payment into your primary currency, or if you want to create a new balance with that currency inside your account.
So IMHO as long as you directly change the incoming currency, you'll never have any USD in your bank balance if you are using PayPal. But you'll want to check out if it's really allowed that way (I'm not a finance lawyer).
2.) Freelancing platforms
I think the big freelancing platforms will take care of that problem for you. Atleast oDesk has a method which they call LFT (Local funds transfer) which means that the bank of oDesk will care for the currency exchange (again you'll loose some money, because they make profit with the exchanges rates just like PayPal does), but you'll directly receive money in your currency to your bank account and you'll never see any USD. If you plan to use a freelancing plattform to reach your customers anyway, you may have a look at that.
3.) Western Union
Another possibility (and pretty common as a payment method for offshore work in the US as far as I know) is Western Union. Your client will be able to directly pay in USD and Western Union will automatically exchange the money into your currency, before tranferring it to your bank account, so you'll not directly receive any USD this way, too.