How can a dual citizen of Israel and Russia travel to the "Arab Boycott" countries without getting into trouble?

My friend is a dual citizen of Israel and Russia, who was born in Russia and lives in Israel. He would like to travel to some of the countries which currently boycott Israel. Obviously this is a risky endeavor since double-citizens from Israel have been involved in spy plots, which makes it highly unrecommended to get caught holding a second Israeli passport.

What are the steps he should take to have a safe journey? Some of the possible issues include:

• Place of birth. In this scenario everything is okay, since it's not in Israel.
• Where the Russian passport was issued. This is also okay, since it was issued in Russia.
• Getting the right passport stamps before entering the destination.
• Getting a visa (where Russian citizens can't go visa-free).
• Storing the Israeli passport while making the journey.
• Avoiding violating the Israeli law on visiting "enemy" countries.

Note that this question is not a duplicate of "I have two passports/nationalities. How do I use them when I travel?", since it's about a specific issue which only affects Israeli citizens.