First things first you need to contact the correct authorities. You require written permission to trap crayfish in the UK.
There was an episode of River Cottage where they trapped them on the River Kennet. The Gov website doesn't list where you can or cannot trap signals, as you need landowners and angling club permission to trap on our lakes and rivers.
If you trap crayfish without written permission you could be prosecuted.
Bonus however of the fact that the crayfish licence is free currently.
For the traps you must follow the guidelines set out by Gov.
Crayfish trap rules
There are strict rules about the design and size of crayfish traps because they can harm other wildlife. If traps are the wrong size or design your application will be refused.
- be no longer than 600mm
- be no wider than 350mm at the widest point
- have an entrance no more than 95mm wide
- have mesh no bigger than 30mm at its widest point
- have EA identity tags
- tell EA or NRW about crayfish you trap using a catch return form (you get the form when you’re authorised)
- return species not covered by consent to the water they came from
As for the native species, these can be trapped soley for scientific research, and you again require written authorisation to do so. If you trap by accident simply return to the water where you found it, there won't be harm to them if they are trapped by accident, they just get a free meal off you.
Be aware when catching an invasive species you cannot release it back into the wild, it must be kept, or killed.
Source: Gov.uk trapping permission pages