Topical application of caffeine:

caffeine, which is known to have antioxidant properties, impedes keratinocyte proliferation and migration, suggesting that it may have an inhibitory effect on wound healing and epithelialisation.

Oral consumption:

Daily consumption of caffeine impairs graft viability when given in medium dose and increases collagen synthesis, irrespective of dosage. This study was in experimental rats; the results are not directly translatable to humans.

On the topic of collagen synthesis, I decided to find a study about it, not to leave the topic unfinished, here’s what I found:

Caffeine reduces collagen synthesis in human cultured skin fibroblasts.

Based on all my findings, I would personally suggest avoiding caffeine altogether if you’ve a healing wound.