I am a dual citizen of Malaysia and Canada. Malaysia does not allow dual citizenship.
If I apply for a US tourist visa in Malaysia using its passport while declaring that I am a Canadian dual citizen and provide its passport number on the visa application, will the US embassy object to it?
This is tricky situation. You are doing something that isn't permitted so there is no documented process around it.
As a Malaysian citizen, you would need a US visa, requiring you to fill out all 83 glorious pages of a DS-160 form. The form specifically asks about other other citizenships. Lying on the form is definitely not a good idea: if you get caught doing this you will be banned from US entry for a long time.
Chances are your visa application will be handled at some point by the US embassy or consulate in Malaysia. They will know that Malaysia doesn't recognize dual citizenship, but whether they would notify the Malaysian government is anyone's guess.
They may quite likely decline your visa anyway, simply because you don't need one. You have a Canadian passport: just use that. "I like to keep lying about my dual citizenship" isn't a exactly convincing reason for them to issue a visa.
You MAY be able to fly directly without a visa. You can use your Canadian passport to check in for your flight with the airline and use your Malaysian passport at immigration exit control. Whether this may result in you being found out depends a bit on what information the airlines and the government share. This isn't documented anywhere, so you would be taking a risk. I don't have any data to assess the size of that risk. This being said: using different passports for exit at the departure location and entry at the destination is perfectly normal and standard procedure.
The safest option is obviously to fly through a 3rd visa free country and switch passports there.
The only safe answer in this convoluted situation is to go to the U.S. consulate in Malaysia and get an answer from them in writing that you can show to anyone along the way who might give you trouble, except for immigration control when you get back home to Malaysia; they would only get to see your Malaysian passport.
All the ideas about stopping on the way depend on the fact that you stopped not being discovered. There are many ways an immigration official might discover that you stopped on the way. This is one of the things that could, depending on their mood, cause them to "smell" that you're trying to get around the rules. Which you are. This fact will make you more likely to be discovered. As soon as an immigration official finds out there is anything you're hoping they wouldn't find, they will go into "full investigation" mode. You probably don't want this: even if they decide you're OK at the end, it would probably ruin the first day or two of your trip, which you might spend locked up in the airport until they complete their investigation.
Getting an opinion, in writing, from the U.S. consulate should eliminate this problem, since rather than doing something you hope they won't notice, you'd be playing with the rules. The consulate should be willing to help you, as it should be pretty obvious to them that this is a bureaucratic nightmare situation, which is pretty much exactly why they are there. Chances are, they will tell you that all you need is your Canadian passport. You will need to request a letter from them stating that, but hopefully they will realize that it's a sensible request and costs them little, and comply.
