You can execute a binary in Linux without the execute permission. Use /lib/ld*.so or /lib64/ld*.so as an ELF interpreter. The actual name differs from architecture to architecture. ld is the program linker/loader. It finds and loads the shared libraries used by the program and executes it. ld-linux handles ELF binaries.
cp /bin/ls /tmp/ls
chmod a-x /tmp/ls/lib/ld-linux.so.2 /tmp/ls/lib64/ld-linux-x86-64.so.2 /tmp/ls