You can actually decline "manas" to say "mana ranka", "manos rankos", but it's majorly outdated, only to be found in older literature.
The instrumental case doesn't need "su", although you can add it for emphasis. valgau rankomis means virtually the same as valgau su rankomis. But this only works when the instrumental case is used to designate an instrument.
In other uses of the instrumental case you cannot add "su":
einu gatve (walking on/down the street), einu su gatve jis tapo mokytoju (he became a teacher), jis tapo su mokytoju
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