Firstly you can use packages from the 3 series in the 4 series. Open the Puppy package manager and there will be a tab or radio button allowing you to choose to install packages from an earlier series (not sure but I think the 2 series is also an option ).
If the application you want is still not available this is how I install Debian packages (there is probably a quicker and easier way but this works for me) open a terminal and enter "undeb" if you receive an error stating that the command is not found then you will need to download and install "undeb-unrpm" first.
Once you have "undeb" installed open a terminal and navigate to the directory you downloaded the .deb file to and the steps I use are:
1/ Use "undeb" to extract the files from the .deb package.
2/ Make a new directory with the name of the .deb being converted. eg for yourfile.deb
3/ Move all files and directories extracted from the .deb into the new directory.
mv ./* yourfile
mv ./*.* yourfile
4/ If the original .deb package was still in the current directory before everything was moved, move it back out of the new directory.
mv ./yourfile/yourfile.deb ./
5/ Create a tarball of the new directory with exactly the same name as the new directory. This is critical, if the names are not identical the pet package will not extract when the package is installed.
tar cvfz yourfile.tgz yourfile
6/ Convert the tarball to a pet package.
I'm not sure how to set up a menu entry but you can start the application from the command line.