I wouldn't undo the screws then.
Sometimes, especially when a shower is added to a bathroom originally without one, or an extra bathroom is added, the waste pipe run is not very good. e.g. too flat, or too long, bad jointing.
When you tip a bucket of water into the shower tray, how long does it take to drain away?
I'd avoid aggressive chemicals like caustic soda as it can be serious if it splashes onto skin or eyes during later attempts to clear.
if it is soap, detergent and grease sludge (including from the oils in skin creams and hair conditioner), Washing Soda Crystals will break them down. Spoon the crystals into the waste (and overflow if there is one) and when full, add enough very hot water to moisten them, but not to wash them away. Leave overnight and dribble in some more hot water. Don't use a lot of water, and it will stay in any blocked or flat pipes and have a chance at working there too. it is a good idea to do this weekly.
In ceramics like WC pans and basins, don't use boiling water as it may cause cracks.
Soda cleaners will attack aluminium and remove the finish.
If you actually have a blockage already, agitate it with a sink-plunger or, better, sink pump. If there is an overflow, get your assistant to press a damp rag firmly against it to prevent the pressure and suction pulses escaping.
Do this before your soda cleaning, and again afterwards.
In cases where, e.g. someone has been sick in the basin, you may get diced carrots, peas etc coming up. Best to ladle such material into your bucket and tip it down the WC. If there is kitchen roll, sanpro, cotton wool, hairballs, plastic toys, condoms, do not put it down the WC.
this is actually a pump
www.robertdyas.co.uk/catalogsearch/result/?q=sink+plunger
wash your plunger or pump very thoroughly after use.