I was injured at work and had to get stitches, can I still do cardio exercise?

Depends..... Exercising after getting stitches depends on the location of the stitches, depth of injury, and whether or not deeper structures (tendons, ligaments, joints, muscle) were involved. Consult with your doctor for specific recommendations.
Simple suture care. Depends on wear the injury was. Usually the closer the injury to the heart the quicker it will heal. Keep dry for 3-5 days on areas with more circulation but areas like the foot and hands usually keep dry for at least 10-14 days.