A search on Google trends for bigrams involving application and either open, start, launch, run, or execute reveals the following search trends:
Apparently, launch and execute have been somewhat more frequent collocates of application at the beginning of the observation period, but are rarely searched for nowadays. These two may be out as options, then.
Run used to share the top ranking with open, but has fallen out of use somewhat over the last few years. Start shows a rather constant trend, and is now clearly in second place. Nevertheless, open appears to be most frequent search term together with application.
In conclusion, neither run, start, nor open are bad choices. Yet, based on the principle of least surprise, open might be the best candidate.