There are many differences between the fields of aeronautical VS mechanical engineering. Do you have any experience with aviation that drives your preference?
I will only speak about what I know. Canada has MANY young engineers with a degree in mechanical or aerospace engineering. Too many, and most do not get hired in their field. Too many of them do not have any distinguishing features in their skills to make them stand out among others who apply for any engineering job. To bring an engineer from any outside country into Canada to fill a position, for which there are already a surplus of graduates, is hard without bureaucracy and a rigorous justification. The candidate must have special experience or skill that set them apart in a way that cannot easily be found here. If you can extrapolate that situation from Canada to other countries you are considering, then that means an engineering degree does not mean a ticket to work abroad.
That may sound depressing, but there may be hope:
Is electronics something you are no longer interested in?
Or are you interested in preserving your electronics experience in your future work?
Let me extrapolate in a new direction, and see if you are interested:
The blend of the two disciplines "electronics" and "aviation" is called "avionics" and it can be difficult to find people with combined skills in these two disciplines to support avionics equipment design projects or the efforts to integrate new avionics into the existing aircraft systems. From your current position you could study aviation either as a pilot or as an avionics maintenance specialist. Both skills would help enable you to travel around the world. Your electronics background would help you understand the integration of the many systems, making you learn faster as an apprentice maintenance specialist, possibly the same in piloting as you fly more complex aircraft. As a student pilot, you would probably fly a very rudimentary aircraft, but as you pursue flight under instrument conditions (night, fog, cloud) then your understanding of system integration will have to be very sharp to fly the plane well. If you then turn that understanding to the modern challenges of avionics such as precision approach guidance, enhanced vision, and collision avoidance, then you might be able to see yourself having cultivated some very valuable skills. Many professional pilots become adept users of these systems, but only a few get deeply involved in their integration into the aircraft, and yet having piloting experience would give you a tremendous advantage over those who don't. Today, Canada does not have enough specialized maintenance people who have enough insight and skill at installing and integrating advanced avionics, and we must hire overseas to find them. Those are some options to consider, either at the technical or engineering level, that I believe will be in high demand for many years.
Here is the way I see people immigrate to Canada in the MAJORITY of cases: They have specific skills that are in high demand in Canada not being met by the population here. Currently there is a shortage of aircraft maintenance engineers, for both mechanical, engine and avionic systems. This can be addressed by companies when they are allowed to hire applicants from other countries. The case is similar in other industries that have shortages of specific skilled people.