Chain Waxing - Strainer / Colander / Other?
Once you have fully de-greased and waxed the chain, most suggest that you can simply re-dip the chain in melted paraffin  to re-wax, but as you have found out this can leave small particles in the bottom of the slow cooker.

Personally, I just keep a small circular mesh steel plate at the bottom of the slow cooker to keep the chain out of the debris when re-waxing. Then every so often I like to remove the debris from the wax.

Removing debris from the wax

While the wax is liquid in the slow cooker I will pour off wax into a container (usually old yogurt container that has been cleaned). Because it takes time for wax to cool and harden, typically the debris first settle to the bottom prior to the wax hardening.  

Once the wax has hardened I will heat up the outside of the container (e.g., boiling water) to loosen the adhesion of the solid wax to the container so I can get the wax out as one solid chunk. The debris will then be at one end of solid wax piece, making it easy to cut off the wax with the debris.

With the debris removed, I will remelt the remainder of the wax and reuse.

Cleaning chains before re-waxing

Once a chain has been de-greased and waxed, it is much easier to clean than a regular chain that has been lubed with oil. As such, cleaning the chain before re-waxing can ensure you wax stays cleaner for longer before having to deal with debris build up.

There are two main approaches that I know about:


Soak the dirty chain in boiling water, the heat will liquefy the paraffin.  Agitate the chain to loosen debris, then wipe the chain with a clean rag.  This typically gets the chain very clean before re-waxing.  
Ultrasonic cleaner. Molten speed wax has a good tutorial on this approach.  I haven't tried this so I can't comment.


Both approaches are water based (i.e., aqueous) cleaning solutions as such please ensure your chain has had time to dry before attempting to re-wax.  When dealing with boiling water, ensure you use heavy duty gloves to prevent burns.