Sure they will work, but graphite does slowly disintegrate, not via any chemical process, just physical wear from the electrolysis. Also, are they not rather short if from a battery? Their length and diameter may be physically limiting when designing a cell. Graphite gouging rods(no idea what they are for, other than used in welding and available at related shops) are nice long thick graphite shafts with a thin copper cladding that can be peeled off with minimal effort. These can be treated with linseed oil to reduce disintegration. I think I paid 20$ CDN for 50 foot long 1/4 inch rods, but this was a long time ago, and prices likely are up.
Ebay is your friend for Pt, and Ir is no problem. Other sources exist, but ebay was cheap.
I've never ran a perchlorate('back in the day' when I did this I had HClO4, so no effort was made on electrolytic perchlorate production) cell, only chlorate. But for perchlorate, Pt anode and Ti cathode seems common. This electrode config will work for chlorate of course as well with run times controlling product. It is worth noting that with graphite electrodes you will be unable to make perchlorate, but this can be good if you do not want to monitor your cell too much, and only want chlorate to form.