On the page where you speak about Apple® and Safari®, you need to use the appropriate TM, SM, or ® symbol the first time the term apears, plus the following type of statement, usually in the footnotes (assumes distribution outside the US):

Apple and Safari are trademarks of Apple Inc., registered in the U.S.
and other countries.

By googling “apple trademark” I was able to find a list of Apple Trademarks and from there, Guidlines for Using Apple Trademarks. Just about every company has similar web pages. You always need to look them up to see whether product names are trademarked or registered (or serial-marked). Also there are guidelines about how and how not to use these words in sentences, how to use logos, and the relative size and typeface of Apple trademarks compared to the rest of the packaging of your product.

As @JamesSnell asked, why wouldn’t you make your program launch the default browser of the current operating system? Why limit yourself to Sarari and Chrome, presumably only on a Mac?

It is interesting to note that Trademarks (inc. serial marks and registered trademarks) are one of three groups of unrelated (in the US) legal protections colloquially referred to as “Intellectual Property.” The other two are Copyrights and Patents.

Disclaimer: I am not a lawyer, nor a spokesperson for Apple. These statements are not legal advice, but my personal “best guess” at how to use Apple trademarks. Please read the linked documents and use your own best judgement about how to apply Apple’s rules in this and other situations. Better yet, hire a licensed lawyer to advise you.