You have three options:

Bend the pipe cleaners into the shape of spider legs.
(This uses spider as an adjective.)

Bend the pipe cleaners into the shape of a spider's legs.
(This is where the apostrophe goes for one spider.)

Bend the pipe cleaners into the shape of spiders' legs.
(This is where the apostrophe goes if you envisage all spiders.)

Read more about using apostrophes for possession.

This page also includes a useful infographic on the use of apostrophes for possession.

Thank you! this is an amazing website! I've learnt soooo much!