Try the following script;

 ## $1 - Small File
 ## $2 - Large File

 sed 's/^/\//; s/$/\/d/; s/\\/\\\\/g' $1 > $HOME/sed_scpt.txt
 sed 's/\\/\\\\/g' $2 | sed -f $HOME/sed_scpt.txt > $HOME/desired_output.txt
 
 ## Alternatively, you could change the 2nd line with the following;
 sed -f $HOME/sed_scpt.txt $2 > $HOME/desired_output.txt


NOTE: I've used GNU sed 4.2.1.