Defense in general:
You will not be able to defend yourself in any situation if you are not trained for it, as described by TransTerra. That goes for weapons just the same as for martial arts. And that goes beyond being able to shoot a weapon and knowing Karate. It means to be familiar in situations where you would use the weapon and when it comes to contact sports you will have be trained in a full-contact form. The civilized ways of shooting at a range or friendly judo fights are in no way anything that helps you when you get a shotgun held in your face while stopping at a traffic light or if someone grabs you by the neck while flashing a knife while you are looking at a shopping window. Or if a hooker drops you drugs into your drink.
On top of that, a lot of crime in the world is not a 1:1 issue but an issue of gangs operating. So you have to be able to deal with other people in the background as well.
Weapons and traveling:
You will likely have issues crossing borders with weapons. Airplanes and other tightly controlled transport make it basically impossible. You would have to buy one locally and then somehow sell it again before you leave.
Security while traveling:
There are of course many dangerous countries, but the issue with security in other countries is not so much about how well you are equipped or how well you can fight. The issue is much rather when to expect what from whom and how to behave. And for this, you will have to know the country, if not the city itself. While you are discouraged to stop with a car at a red light in some south American countries, some places in Africa are much more an issue of happily waving to the gangs in the street so they know you have seen them. In France it is simply about not using PCs in a Starbucks terrace and in Japan not get drunk in certain areas of the city.
In my experience it is much more easy and simple to stay out of trouble then to be prepared for it. Travel guides as well as local people can often advise you very well where not to go and what not to do.
If you are a high net worth individual you are even then in most cases better off to stay low key if that is possible than to hire guards. In many countries, hiring guards implies an armored car or even traveling by helicopter only. If you can credibly wear a cheap jeans and T-Shirt and leave your diamond watch at home, you will have a higher chance of staying out of trouble than if you have 3 armed men following you.