my 2c, ointment tends to be weak.
go for it from the inside, in therapeutic doses. eg 50mg zinc gluconate (balanced with 2mg copper) per day. gluconate is supposed to be the form least likely to have cadmium contamination (zinc and cadmium are very very similar so it's tough). and don't neglect the copper balancing. therapeutic zinc can interfere with copper status so you have to take copper with zinc for a precaution against copper depletion.
best to take zinc(+copper) in the morning to match zinc's natural circadian rhythm. consuming gluten grains, sugar, dairy, and/or alcohol can interfere with or deplete zinc.
a serum zinc test would be a really great thing to have done if possible. but no supplements right before testing. it clouds the results.
yes zinc topicals are available off the shelf too, eg zinc oxide 18% in medicated 'penaten' lotion. i have no info on how effective topical zinc is on serum levels.
you will probably have to go to a high end specialty nutrition/health store to find a good product. i am currently stuck with zinc citrate 50mg containing 2mg copper. it's pretty good but i want zinc gluconate with the copper blended in - have not found that particular product to date. regardless, i have had great effect with zinc citrate. hope your dad finds it useful too