><> with -v flag, 36 + 2 = 38 bytes

:&\         ~<
"o>l?!;:&:&(?^&~:n&" 

Input the list on the stack with -v so that the first element of the list is at the top of the stack. It will print the dropsorted list with a trailing space.

Test run :

$ for input in "1 2 5 4 3 7" "10 -1 12" "-7 -8 -5 0 -1 1" "9 8 7 6 5" "10 13 17 21" "10 10 10 9 10"; do echo $input '-> ' $(python fish.py dropsort.fsh -v $(echo $input | tac -s ' ')); done

1 2 5 4 3 7 ->  1 2 5 7

10 -1 12 ->  10 12

-7 -8 -5 0 -1 1 ->  -7 -5 0 1

9 8 7 6 5 ->  9

10 13 17 21 ->  10 13 17 21

10 10 10 9 10 ->  10 10 10 10

><> with -v flag, 36 31 + 2 = 33 bytes

:&\o " "&n:~& <
~ >l?!;:&:&(?!^

Input the list on the stack with -v so that the first element of the list is at the top of the stack. It will print the dropsorted list with a trailing space.

Test run :

$ for input in "1 2 5 4 3 7" "10 -1 12" "-7 -8 -5 0 -1 1" "9 8 7 6 5" "10 13 17 21" "10 10 10 9 10"; do echo $input '-> ' $(python fish.py dropsort.fsh -v $(echo $input | tac -s ' ')); done

1 2 5 4 3 7 ->  1 2 5 7

10 -1 12 ->  10 12

-7 -8 -5 0 -1 1 ->  -7 -5 0 1

9 8 7 6 5 ->  9

10 13 17 21 ->  10 13 17 21

10 10 10 9 10 ->  10 10 10 10

Edit : saved 5 bytes thanks to Fongoid

><> with -v flag, 36 + 2 = 38 bytes

:&\         ~<
"o>l?!;:&:&(?^&~:n&" 

Input the list on the stack with -v so that the first element of the list is at the top of the stack. It will print the dropsorted list with a trailing space.

><> with -v flag, 36 + 2 = 38 bytes

:&\         ~<
"o>l?!;:&:&(?^&~:n&" 

Input the list on the stack with -v so that the first element of the list is at the top of the stack. It will print the dropsorted list with a trailing space.

Test run :

$ for input in "1 2 5 4 3 7" "10 -1 12" "-7 -8 -5 0 -1 1" "9 8 7 6 5" "10 13 17 21" "10 10 10 9 10"; do echo $input '-> ' $(python fish.py dropsort.fsh -v $(echo $input | tac -s ' ')); done

1 2 5 4 3 7 ->  1 2 5 7

10 -1 12 ->  10 12

-7 -8 -5 0 -1 1 ->  -7 -5 0 1

9 8 7 6 5 ->  9

10 13 17 21 ->  10 13 17 21

10 10 10 9 10 ->  10 10 10 10