Is there an alternative to DVD-Shrink, that can compress a DVD image to a smaller size to fit on a writeable DVD?

The 2 best tools I know of that work are dvd95 and k9copy.
sudo apt-get install dvd95 or sudo apt-get install k9copy
installing k9copy on a non-kde system will pull down a lot of dependencies, which may or may not be an issue with you.

The best one out there is k9copy but I've been having issues with it in 12.10 64bit, a good alternative is dvd95 and there's another app called xdvdshrink though xdvdshrink's subtitle ripping capabilities seem broken.

Another option for you would be to run dvdshrink through wine. I have been able to do this rather easily, the only thing extra needed is to list your cdrom in your fstab file and then also add the drive in winecfg as well.

Start by running this command:

sudo mkdir -v /media/cdrom

This will make the directory where your cdrom will be mounted. Then run this command to open fstab with gedit as root.

gksudo gedit /etc/fstab

Here's the fstab line needed to mount the cdrom, simply copy and paste it to the end of your fstab file:

# built in CDrom
/dev/sr0    /media/cdrom    auto    ro,noauto,user,exec 0 0

Run this command:

sudo mount -a

Then run:

winecfg

Here's a picture of where to add drives in winecfg just click the drives tab, then the autodetect button. Then apply, and OK.

HandBrake

HandBrake is really good, and this is the tool I recommend.

The download is available at https://handbrake.fr

Better yet, there is a PPA at https://launchpad.net/~stebbins/+archive/handbrake-releases/

Although the PPA for the most recent release (version 9.9) is for Raring, it works just fine in 14.04. You can add the HandBrake repository for Raring and install HandBrake in Ubuntu 14.04 as follows:

echo "deb http://ppa.launchpad.net/stebbins/handbrake-releases/ubuntu raring main" | sudo tee -a /etc/apt/sources.list.d/handbrake.list
echo "# deb-src http://ppa.launchpad.net/stebbins/handbrake-releases/ubuntu raring main" | sudo tee -a /etc/apt/sources.list.d/handbrake.list
apt-key adv --keyserver keyserver.ubuntu.com --recv-keys 816950D8
sudo apt-get update
sudo apt-get install handbrake-gtk

K9Copy

K9Copy was an excellent tool, but the developer had stopped supporting it years ago. Apparently another developer has picked up the project just recently (http://k9copy-reloaded.sourceforge.net/#start) and released version 3.0.0, if you want to try it. I haven't tried it myself, so I do not know if it will work in 14.04. You will have to build it from scratch, since pre-built packages for the new version are not available yet.