Firstly the idea of a bottle trap is that you don't have to remove it to clean it, the bottom should come completely off and cleaning is a doddle as a result.
Assuming you have to remove the thing, getting rid of the pedestal is an advantage, but involves quite a bit of work.
Some pedestals are well under the sink and you will need to raise the front of the sink by as much as 10cms. It depends on the curvature of the sink bottom. This means disconnecting both taps from their pipes to allow the bowl to move freely. You also have to loosen the wall bolts to let the sink move. So you disconnect the taps from their pipes and then loosen the sink from the wall. Pull the pedestal out.
Try to keep the putty like stuff on the top of it as it forms a seal between the sink and pedestal. Unless it is a massive sink you may not have to support it. The pedestal is to provide support for people leaning on the sink when using it.
As they practically give bottle traps away with corn flake packets, don't bother cleaning it, go buy a new one. also get two 15mm fibre washers to replace the ones inbetween the taps and their pipes. (Assuming you have metal pipes and the usual metal tap connectors)
If you didn't manage to save the putty like stuff on top of the pedestal you will need some new. This can be plumbers mait or putty.
All these instructions are very subjective and you may be able to leave some out. Start by loosening the sink bolts and see if the pedestal can be moved. Then keep loosening as necessary to remove it, up through removing the pipes from the taps.
With my large and heavy sink the trap is right inside the pedestal.
I don't fiddle about with it. I disconnect the taps and waste pipe and then remove the sink and trap and plonk it upside down in the bath to work on it.
I would replace the trap with a HepVO type. These employ an internal flexible tube rather than a water seal. The idea is that when no water is flowing through, the tube is collapsed forming a seal. Water going by opens it. I've used several of them and they work as advertised. They don't have the problems of blocking that bottle types have.
Have you identified the cause of the blockage? Hair is a very typical one if you have people and teenagers with long hair using the sink.
Yes you should try to support the sink in some way.
If its blocked due to normal build up of gunge as opposed to someone dropping something solid down it have you tried caustic soda? There are not many blockages it won't clear given time.
Had a similar problem recently. Went fishing through the plug hole with a long piece of fine, stiff wire bent into a hook at the end. Caught two cotton buds that wouldn't go round the 'bend' and were the origin of the blockage, and a mass of hair, toenails, soap gunge, etc. etc. etc.......All clear now though.
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