I just tried installing wkhtmltopdf to shared hosting and it seems possible to run it. All you need is a bit of knowledge of Linux commands. Here is what I did:
Connect to your DreamHost account first, via ssh. Then from the server download the software and unpack it:
[dreamhost server] $ wget https://github.com/wkhtmltopdf/wkhtmltopdf/releases/download/0.12.4/wkhtmltox-0.12.4_linux-generic-amd64.tar.xz
[dreamhost server] $ xz -d wkhtmltox-0.12.4_linux-generic-amd64.tar.xz
[dreamhost server] $ tar xvf wkhtmltox-0.12.4_linux-generic-amd64.tar
You'll have a new directory wkhtmltox with a /bin subdirectory in it. Change into that directory and run ./wkhtmltopdf.