The fuse in a UK plug is really largely there because of the ring-circuits i.e. the socket might only be fused at 30Amps or 32Amps.
On the continent, socket circuits are fused at 16Amps normally, sometimes 10amps (older wiring).
Just cut the UK plugs off the appliances, and wire on Schuko plugs, if you need help on doing this consult a local electrical shop, electrician or someone who is familiar with wiring plugs.
Remember though, it's a little less common to wire plugs on the continent as they've had molded-on plugs as standard for MUCH MUCH longer than the UK.
However, it is usually still possible to buy plugs in most hardware shops and even supermarkets.
With small, appliances that do not require an earth, up to 2.5Amps (575W) max you can use
For all other appliances, you need to use a CEE 7/7 plug
Wiring either of these is pretty simple - if you need help, I'd suggest asking a Dutch person who has some clue about wiring.
European sockets are not polarised, i.e. it doesn't matter which way the live and neutral go.
Earthing is done with scraping contacts on the sides.
Normally, on rewirable plugs, the live and neutral are the two outer terminals and the earth will be a centre terminal.
No modern appliances will have any issue with non-polarised sockets, the only thing you should remember is that if you are servicing an appliance you should ALWAYS remove the plug from the wall socket, not just switch it off as there is always a risk of live internal components.
Also, if you're changing light bulbs in lamps, plug them out first.
Never assume that everything is dead in an appliance simply because it is switched off.
(This is equally useful in advice in the UK)
With regards to overloading a circuit, you won't be able to. the MCB will trip / fuse will blow once you go over 16amps and there are no appliances for normal use in the UK that are rated more than 13 amps so that's highly unlikely.
Overloading is more of an issue if you're using multi-way adaptors and power strips all plugged into a single socket outlet and you have tampered with the house's fusing !