Starter relay question

You are fine (so far as current). That solenoid does not draw very much. The main reasons "Ma" used the starter relay was --to make a workable neutral safety switch for automatics, and to lesson the load on the ignition switch contacts because the 'big ol' OEM gear reduction starters had a heavy solenoid load

If however you have an automatic and not a stick, you will either have to have a NSS through the shifter, or install a relay to operate through the NSS on the transmission. You do not HAVE to use an OEM relay. You could also use a more modern Bosch style relay