You can use 'J' and 'K' keys to perform left- and right-click actions.
You can use 'D' and 'F' keys to change paint colors.
This update is for laptop users who play with a touchpad instead of a mouse.
Updated controls can also be found in the manual while playing.
Summary - Alternative control
Actions
Keyboard alternative controls
Left click - Open tiles
Right click - Paint tiles
Select previous color
Select next color
Zoom up
Move camera
'J' key
'K' key
'D' key
'F' key
'Z' + 'J'
'Z' + 'F' + Drag touchpad