Is it okay to hold dumbbell in right hand for right leg squats, and vice-versa (it feels most comfortable for me). Or should I use 1 dumbbell for each hand?
Sounds like you are using the dumbbell to stabilise yourself but in a way that isn't great. Rather than using your stabilising muscles to help you pistol squat you are using a weight to offset the need for balance. The whole point of the pistol squat is really to develop stabilisation (more on this later). By using a 1-sided dumbbell you are potentially sabotaging your own progress.
If you want to add weight onto the pistol squat then you should use either the arms straight position:
or the goblet position once weights get a little heavy:
If you are struggling to do a un-weighted pistol squat because of balance only then use the opposite arm to stabilise yourself against a wall.
Note: Pistol squats re cool but they are not the progression from body-weight squats. They are more of a progression cul-de-sac, they aren't great for building more strength and focus more on developing stabilisation/balance.
The normal progression from a body-weight squat is a single leg step-up: https://www.youtube.com/watch?v=487aR3A7HvM
After that is mastered then a deep-leg step-up: https://www.instagram.com/p/1jdRZorwdE/
If you can do a set of 10 of these you really are going to have to look at using a barbell to progress into higher strength levels
Trickiest part of doing one-leg squats is balance and being able to push more weight is not the main goal of the exercise (you could do regular squats for that). Very few people manage to do single full one-leg squat - your gluteus almost touching the ground with one leg extended.
And even fewer can make a meaningful set of many reps like that. And you definitely need both of your arms for balance. If you don't do full one-leg squat, focus on going the whole way (you can google for videos / articles for "Pistol squats"). However if you do manage to get many full one-leg squats and they feel too easy, you can try to grab and hold a dumbbell with both hands in front of your chest. And definitely shoot a youtube video - it will be impressive to see :)
Okay, there are few things to keep in mind. Symmetry and load distribution. While the whole weight of the dumbbell and your body rests on the one leg you are using, and you are feeling comfortable, your body is not having the center of weight properly balanced through the line of symmetry. Though, it's okay in case of exercises like bicep curls and shoulder flys, in case of squats, having both hands involved gives you better stability. As you responded to my comment saying you are planning to go higher, why not use a barbell, or a kettlebell? As you go heavy, concentrating the weight on one side of the body will disturb the balance and may lead to injuries.