Separate precious metals from catalytic converter
Let me try to talk you out of it ;-)

The precious metals in a catalytic converter sit in a honeycomb ceramic that contains a lot of synthetic Cordierite. This material isn't only heat-resistant, but also quite hard.

Industrial recycling of catalytic converters typically starts with


dismantling (decanning) the ceramic monolith using guillotine shears
breaking down the ceramic to smaller pieces in hammer mills connected by a closed tubing system
milling the material to dust in a ball-mill blender


You might want to wear a filter mask during these steps.

Industrial recycling almost exclusively uses pyrometallurgical tretment (melting the metals) then. 

Having ruled that out, there are two other options:


hydrometallurgical treatment
In order to separate the metals from the ceramic, you can either try to  


dissolve the ceramic in hot alkaline solution in a closed reactor under pressure (to reach temperatures above 100 °C). This leaves the metals intact.  
leach the metals out by using strong oxidizing acids, such as mixtures of concentrated nitric and hydrochlorid acid. You have the metals in solution now.


What are your plans for personal protection during these steps and for the waste water management?   
biomobilization
There is some ongoing research to replace the unpleasant conditions of hydrothermal treatment with microorganisms that can leach the solid metals and store them. As an example, have a look at an article by Helmut Brandl, Stefan Lehmann, Mohammad A. Faramarzi, and Daniel Martinelli, published in  Hydrometallurgy, 2008, 94, 14-17. The authors examined, whether metals could be converted to cyanido complexes, such as $\ce{[Pt(CN)4]^{2-}}$, by cyanide-producing microorganisms. A PDF of their article, titled Biomobilization of silver, gold, and platinum from solid waste materials by HCN-forming microorganisms is available at no cost from ZORA (Zurich Open Repository and Archive). In the case of platinum, however, the results were rather disappointing.