I have an application a part of which uses shared libraries. These libraries are linked at compile time.
At Runtime the loader expects the shared object to be in the <
You are probably looking for some form of delay library load on Linux. It's not available out-of-the-box but you can easily mimic it by creating a small static stub library that would try to dlopen needed library on first call to any of it's functions (emitting diagnostic message and terminating if dlopen failed) and then forwarding all calls to it.
Such stub libraries can be written by hand, generated by project/library-specific script or generated by universal tool Implib.so:
$ implib-gen.py libxyz.so
$ gcc myapp.c libxyz.tramp.S libxyz.init.c ...