Just use ksh (ksh93 precisely), which supports floating point arithmetics natively: 

 $ cat test.ksh
 #!/bin/ksh 
 min=12.45
 val=10.35 
 if (( $val < $min )) ; then 
 min=$val
 fi
 echo $min
 $ ./test.ksh
 10.35

Edit: Sorry, I missed ksh93 was already suggested. Keeping my answer just to make clear the script posted in the opening question can be used with no change outside the shell switch.