My first solution I came up with involved substring replacement including a helper string added before and after the real string. This works as long as that helper string does not appear anywhere in the original string.

:: Trims whitespace at beginning and end of a string.
:: PARAM
:: 1 string to trim
:: RETURN String trimmed string
:TRIM
SETLOCAL ENABLEEXTENSIONS ENABLEDELAYEDEXPANSION
SET HLPSTR=#####%RANDOM%#####
SET STR="!HLPSTR!%~1!HLPSTR!"& SET STR=!STR:~1,-1!
:TRIM_INNER_LOOP
IF "!STR:%HLPSTR% =%HLPSTR%!" NEQ "!STR!" (
    SET STR="!STR:%HLPSTR% =%HLPSTR%!"& SET STR=!STR:~1,-1!
    GOTO :TRIM_INNER_LOOP
) ELSE IF "!STR: %HLPSTR%=%HLPSTR%!" NEQ "!STR!" (
    SET STR="!STR: %HLPSTR%=%HLPSTR%!"& SET STR=!STR:~1,-1!
    GOTO :TRIM_INNER_LOOP
)
SET STR="!STR:%HLPSTR%=!"& SET STR=!STR:~1,-1!
ENDLOCAL & SET RESULT="%STR%"& SET RESULT=!RESULT:~1,-1!
GOTO :EOF

So after thinking about that for a while (~10 seconds), it came to my mind that I do have a way to retrieve the first or the last character of a string. So this solution followed:

:: Trims whitespace at beginning and end of a string.
:: PARAM
:: 1 string to trim
:: RETURN String trimmed string
:TRIM
SETLOCAL ENABLEEXTENSIONS ENABLEDELAYEDEXPANSION
SET STR="%~1"& SET STR=!STR:~1,-1!
:TRIM_INNER_LOOP
IF "!STR!" NEQ "" (
    IF "!STR:~0,1!" == " " (
        SET STR=!STR:~1!
    ) ELSE IF "!STR:0,1!" == "	" (
        SET STR=!STR:~1!
    ) ELSE IF "!STR:~-1!" == " " (
        SET STR=!STR:~0,-1!
    ) ELSE IF "!STR:~-1!" == "	" (
        SET STR=!STR:~0,-1!
    ) ELSE (
        GOTO :TRIM_INNER_LOOP_END
    )
    GOTO :TRIM_INNER_LOOP
)
:TRIM_INNER_LOOP_END
ENDLOCAL & SET RESULT="%STR%"& SET RESULT=!RESULT:~1,-1!
GOTO :EOF

What you cannot see: I compare against space and then against tab. But I disliked the horrible IF-ELSE comparison stuff and ended with replacement check against a whitespace-string:

:: Trims whitespace at beginning and end of a string.
:: PARAM
:: 1 string to trim
:: RETURN String trimmed string
:TRIM
SETLOCAL ENABLEEXTENSIONS ENABLEDELAYEDEXPANSION
SET STR="%~1"& SET STR=!STR:~1,-1!
:: whitespace is space and tab
SET WHITESPACE= 	
:TRIM_INNER_LOOP
IF "!STR!" NEQ "" (
    IF "!WHITESPACE:%STR:~0,1%=!" NEQ "!WHITESPACE!" (
        SET STR=!STR:~1!
        GOTO :TRIM_INNER_LOOP
    ) ELSE IF "!WHITESPACE:%STR:~-1%=!" NEQ "!WHITESPACE!" (
        SET STR=!STR:~0,-1!
        GOTO :TRIM_INNER_LOOP
    )
)
ENDLOCAL & SET RESULT="%STR%"& SET RESULT=!RESULT:~1,-1!
GOTO :EOF