Is there any open-source way to make a static from a dynamic executable with no source code availability?

You can solve your problem in another and more simple way:

Use ldd on your executable to see the linked libraries, for example:

$ ldd /bin/bash
linux-vdso.so.1 =>  (0x00007fffb2fd4000)
libtinfo.so.5 => /lib/x86_64-linux-gnu/libtinfo.so.5 (0x00007fac9ef91000)
libdl.so.2 => /lib/x86_64-linux-gnu/libdl.so.2 (0x00007fac9ed8d000)
libc.so.6 => /lib/x86_64-linux-gnu/libc.so.6 (0x00007fac9e9c6000)
/lib64/ld-linux-x86-64.so.2 (0x00007fac9f1e1000)

Then collect all the libraries in a folder and set the LD_LIBRARY_PATH environment variable before running your program to point at this folder:

$ LD_LIBRARY_PATH="/opt/my_program/lib" /opt/my_program/start

Alternatively you can add an entry for the lib folder to /etc/ld.so.conf.d/. But that would apply the change systemwide.

One suggestion regarding statifier:

If address space layout randomization (ASLR) is causing it to fail you don't have to turn it off for the whole machine. You can turn it off just for that process:

$ setarch `uname -m` -R statified_pdfedit [args...]

It'll run that command with randomized layout disabled (no need to be root).