Safe amount of current going into my device?
The Sparkfun logic level converter outputs voltage, not current. It can output a maximum of 220 mA to an output that is drawing that current, but will not "push" a current anywhere. It should probably be safe to use for this task.

That being said, a more appropriate part for this task would be a buffer IC, like the 74HC244 (octal tristate buffer, 3.3V CMOS compatible inputs when running at 5V). There's nothing wrong with the Sparkfun level shifter, but this part should be easier to source and use in a professional design.