I have the same width wheels on my car and have run both tyre sizes. The 235/40 will be closer in rolling diameter to factory, therefore your speedo will be read more accurately than with a 245/40.
In saying that, I have a 245/40 at the moment, handling difference is probably not even noticeable between the 235 and 245, especially for daily use, but running staggered tyres should balance out the understeer/oversteer.
I'd suggest once you fit your new tyres, if you're not comfortable with the way it handles get a good wheel alignment at proper suspension specialist, talk to them about what you're feeling with the car and get the alignment adjusted to suit your preferences.