#Japt, 35 32 22 20 16 15 bytes

¡Y?(F-XnG)sG :X

Explanation:

¡                 //Take input and map (shortcut to "Um@"). Input should in the form of "#123456"
 Y?               //if Y is not 0, then return (F-XnG)sG, otherwise last step...
    F-XnG           //Subtract X, converted from hexadecimal (G is 16) to decimal, from 15
          sG        //convert decimal to hexadecimal
             :X   //...otherwise return X unchanged (happens only with #, the first char)

Japt, 35 32 22 20 16 15 bytes

¡Y?(F-XnG)sG :X

Explanation:

¡                 //Take input and map (shortcut to "Um@"). Input should in the form of "#123456"
 Y?               //if Y is not 0, then return (F-XnG)sG, otherwise last step...
    F-XnG           //Subtract X, converted from hexadecimal (G is 16) to decimal, from 15
          sG        //convert decimal to hexadecimal
             :X   //...otherwise return X unchanged (happens only with #, the first char)

#Japt, 35 32 22 20 16 bytes

Ur"\\w"@F-XnG)sG

Explanation:

U                   //input. Should in the form of "#123456"
 r..............    //.replace()...
  "\\w"             //...any alphanumeric char (i.e. all but the #) with..
       @........    //anonymous function with parameters X,Y,Z (actually only first used)
        F-XnG       //Subtract X, converted from hexadecimal (G is 16) to decimal, from 15
              sG    //convert decimal to hexadecimal and return the result to @...

#Japt, 35 32 22 20 16 15 bytes

¡Y?(F-XnG)sG :X

Explanation:

¡                 //Take input and map (shortcut to "Um@"). Input should in the form of "#123456"
 Y?               //if Y is not 0, then return (F-XnG)sG, otherwise last step...
    F-XnG           //Subtract X, converted from hexadecimal (G is 16) to decimal, from 15
          sG        //convert decimal to hexadecimal 
             :X   //...otherwise return X unchanged (happens only with #, the first char)

#Japt, 35 32 22 20 16 bytes

Ur"\\w"@F-XnG)sG

#Japt, 35 32 22 20 16 bytes

Ur"\\w"@F-XnG)sG

Explanation:

U                   //input. Should in the form of "#123456"
 r..............    //.replace()...
  "\\w"             //...any alphanumeric char (i.e. all but the #) with..
       @........    //anonymous function with parameters X,Y,Z (actually only first used)
        F-XnG       //Subtract X, converted from hexadecimal (G is 16) to decimal, from 15
              sG    //convert decimal to hexadecimal and return the result to @...