Mac OS X with swap turned off uses 6 GB of space in a few hours of heavy use
First, if you want to free up some more space, I used xSlimmer.  It delocalizes AND gets rid of the "Universal" code that isn't used by Intel processors.  This makes all the Apps smaller.  Depending on the number of Apps you have installed you may only see another couple Gigs freed up.

Chrome is caching websites to your disk.  That's part of what it does to "speed up" page viewing.  Most people don't spend all day going to new websites.  They go to websites they are familiar with.  So Chrome (and other web browsers) cache to your hard drive.  Since material is pulled from the local disk, it "speeds up" the page view.

Quite honestly, this is not a "problem" (per se).  This is expected behavior.  You need to either remove unused programs, remove (or compress) unnecessary data files, or increase the size of your HD.  There's really not another option.  Programs may use hard drive space for other functions (auto saving is an example).

It's actually not a great idea to turn off your swap.  Now there are some exceptions to this, I have 16 GB of RAM and didn't Swap once in 30 days.  I have years of experience and decided to shut off my Swap temporarily.  That was a month ago.  No problems yet.

I'm not trying to sound condescending, you may know more about Swap files than I do (you may have invented them).  I'm just saying that usually this is not a good idea.  And if your system really only (yes, only) has 4GB of memory, you are going to cause yourself out of memory problems, or software crashes.  I know because my Mac Mini swaps all the time using 4GB.