Sorry for not responding earlier but the weekend got in between. I presume that you ship the printing DDP, meaning that you are responsible for the importation.
To avoid any mishaps most distance seller sell DDU, so the client has to pick up the parcel at the postoffice and settle the VAT and additional expenses.
If you wish to avoid the handling fee, you have to adopt a completely different distribution/supply system e.g. you register for VAT in one of the EU member states, handle the import in bulk, and have the goods forwarded from thereon. However, if you exceed a sales threshold set for distance selling (big member states 100.000 Euro) you have to register for VAT in that other Member state and pay local VAT on your supplies.
I don't see what registering in other EU member states will add for avoiding paying the handling fee. I presume that the handling fee is due as the mail company is acting as customs agent. I know that if you add a so called greeny (statement on the value of the shipment) to your shipment and the goods are valued under a certain amount, they can just pass as postal package.
This is more a distribution issue than a VAT problem. If you wish more details, please refer to companies like DHL, for further specific help.