Stick shift without clutch may be difficult but a sequential stick shift may be possible... not the standard seq stick shift of performance cars....
Students participating in shell eco marathon used to use bike engines which has sequential gearbox... One of the teams had the clutch bar installed on the gear stick shift they had brought in the cabin..... Shifting would be easy but starting from stand still in traffic may be tricky.
Otherwise i think you are referring to audi or nissan (not sure) that came up with clutchless stick shift short time back.. read an article, but forgot who did it.
There has to be something to depress the clutch if u are using a manual transmission, so it can be either ur foot (the pedal) or the clutch bar of bike installed on the stick like i told above (the hand). If u are looking to totally remove clutch then it not possible