Lighter fluid should be fine for your shutter. At least it's worked well for the dozen or so that I've cleaned. You can use alcohol for the lenses, but my favorite is those little kits in the bubble packs that contain a red plastic bottle of cleaning solution, some lens paper, and a squeeze blower w/ a brush. Bought mine 11 years ago, and I'm still using the same little bottle of fluid. If you need to soak the shutter in high test alcohol to free it up you can safely leave the elements in if you wish. I've had to do this lots of times with the Agfa shutters when the focus was gummed up and you couldn't unscrew the glass. There is no choice w/ those, as you have to soak everything together as it will not come apart. An overnight soak in a coffee cup filled w/ high test alcohol is the only method that has worked for me w/ those. After soaking in the alcohol, the front element unscrewed easily by hand.
I like the method that Whiteymorange describes. To avoid the potential leakage between cells, you could always set the lens in a shallow pan of cleaning solution and do one side at a time.