I've seen some wizards be pretty creative in getting stuff to run on DreamHost, but my reading of the "Installing+Dependencies" link you provided makes me doubtful you will be able to install SWiK on a DreamHost shared server.
1) The document says that Java is required, and Java is not available on DH shared servers. Installing it yourself may, or may not be possible".
2) The first two "Notes" in the "Step by step instructions for downloading and installing components" are another problem in that a) you can't "make a directory called /usr/local/work and do your downloads and installations from there", so you would have to develop your own work-arounds for your need to deviate from the installation instructions, and b) you do not have the ability to "run as root" on DH shared servers, so, even if you "can run much of the configuration without the privilege", since you cannot "do sudo accordingly" for the other steps of the process, this is a problem
3) The documentation states "The httpd.conf will be configured later, when setting up and deploying the wiki." On a DhreaHost shared server, you will not be able to do this, nor will you be able to "restart" the apache server, which is called for in later steps.
I'm not willing to say that it could not be done, but it certianly can't be done using their instructions, and I'm not sure how to approach attempting a "workaround" installation method.