basically manual installation should be the same. Before I realised that it was at debian I installed quanta/koffice manually and it worked more or less the same. If you have a copy of a debian package then make a directory to place the file in. I know that knoppix stores alot in /usr/share e.g. /usr/share/tomcat5. I installed netbeans in /usr/local/netbeans.I think the /usr/ directories are global, but I am not sure but you can google Linux filesystems to find out where to create your installation directory. Then do dpkg -i <package name> and it should install as if you had done it over the net in the directory that debian would usually choose. I think the net connection is only for ease of download. however, when I had to install quanta it didn't tell me that I needed cervisia until I had installed and loaded it. with a manual install this meant trawling through the net to find the package. however with Koffice I found all the support packages there at debian but it was a pain copying them all. If the required support packages are not installed then you will get a broken packages error message with some indication of what packages are needed to get the software to work

If the package is RPM or Slackware or whatever then do alien --to-deb <package name> . then do dpkg -i <package name>

mkdir /mnt/usr/share
cp /mnt/cdrom/tomcat5675687.rpm /usr/share/tomcat5
alien --to-deb /usr/share/tomcat5/tomcat5675687.rpm
dpkg -i /usr/share/tomcat5/tomcat5_9_7.deb

Knoppix has stuff for unzipping zip files e.g. unzip tar.gz, but I am not sure what else (e.g. unzip wapide1.0.zip). The files will unzip to whichever directory you are in at the time.
Netbeans with jdk5 was a bin file and installed by changing permissions and then executing the bin file (instructions were on the download site)e.g.
cp /mnt/cdrom/jdk1.5_67-nb-linux.bin /usr/local/.java
chmod 755 jdk1.5_67-nb-linux.bin
./jdk1.5_67-nb-linux.bin.
So having an internet connection is not essential but makes life alot easier. Could you not take your box to a friends house plug in there and download as you don't need to install software to connect to the internet. (you may have to do KNOPPIX---Network----ADSL/PPPOE and install the relevant driver for your box then do netcardconfiguration)