On the sites of the Dutch organizations which offer 'wadlopen' they often mention a list of items you need to take and/or organize when you go with them.
First of all, in this region the water will always be cold, the mud underneath is always a given and cold weather and rapid changes of weather are common.
- No long trousers, they will only get wet and stick to your legs, making you miserable. Short shorts or swimwear bottoms depending the local acceptable alternatives.
- Shoes are a must and will get completely wet and will likely be very hard to impossible to clean, the suggested footwear is cheap high canvas shoes, here known as basketball shoes, which come up over the ankle and lace up all the way. These are usually cheap enough that most people will throw them out after the event, but they can be washed in your machine with your sturdy clothes, they will likely become clean enough to use again for rough work.
Sandals, wellington type boots and hiking boots are not a good choice for several reasons.
- Warm tops, in layers so you can adjust. One layer should be a wind/waterproof jacket. With your legs being cooled down in the water you will need to keep your top half warm. Clean clothes in a waterproof bag or left on the coast in a round trip or brought to the end of the hike by a one way hike to an island. This is because it is not unlikely that you fall over or get wet in an other way and you will need to put on clean (long) bottoms and might really want to put on clean tops.
- Enough food, and a good part of it the kind that restores calories which you expend while hiking in the cold conditions. Ideally you should bring enough that you have enough for an extended stay (hours, maybe the night) on a sand bank in an emergency.
- Bring your gear in a backpack, so it is high out of the water unless you have to wade through a deep channel.
As stated in the question you should never attempt this without a guide who is experienced in the area and has means to communicate with rescue services, but it does not hurt to have your (smart) phone in a waterproof cover somewhere in your backpack, so if the guide gets in trouble, you can call the emergency services, even better if you have a gps and can give a good indication of where you are.
Anytime you get onto a mud flat, just of the coast as well, know the tide times and make sure you can return well before the water comes in. Never attempt it alone (even if the others stay on the coast they can call for rescue if you get stuck.)
Remember that the tide coming in will, in many cases, come higher than your head if you stand on the mud, in case of falling down or getting stuck lower than mud-top level, you stand even less chance. And the tide can get in as fast as a horse in gallop, (whatever speed that is, it is faster than you can walk.)