Introducing dogs on leash is a REALLY bad idea. Dogs, in general, are more reactive on leash, because they can't present to each other with normal body language, which tends to make both dogs pull and get worked up. The only way two on-leash dogs can approach is nose to nose, which dogs would NEVER normally do. They approach side to side, each sifting the other's rear as they circle. Then if the leashes get tangled if they TRY to circle, it can cause them to panic and get in a fight where none was intended.
If you think there is cause for concern that your dog might start trouble, first take them on a parallel walk, each dog attached to a separate person, without letting them interact. Then, if all seems well, introduce them with one inside and expen and the other outside, and watch their behavior. still not ideal, but it does keep them safe from each other.
In most cases, if dogs have reasonably good social skills, it is best to let them get to know each other loose, in a neutral location. Honestly, we have Havanese play dates on a regular basis in my large fenced back yard. Some of the dogs know each other, but we have some new comers every time. I always have an expel or tow set up for time-outs, but they rarely get used. Shy dogs often want to sit on their owner's lap or under their chair to start with, and we don't push them. Eventually, almost all get down and want to interact with the other dogs when they feel safe.
The ONLY dogs who have ever needed the "time out" pens have been two specific intact males, who sometimes get blustery with each other. Even then, I wonder whether there have been "girly smells" that set them off, since there are often at least some breeders present. We ask that bitches in heat stay home, but even the SMELL of a bitch in heat on someone's clothes can make certain boys get pretty puffed.