First be aware that boys are very often quite behind girls on their fine motor skills so you can't compare them. Your son is ambidextrous and this is a wonderful skill. My husband writes and cuts with one hand and plays sports, eats, and everything else with the other hand. You don't want to make him choose a hand, this will likely lead to him being less proficient than he would otherwise be. Instead give him lots of exposures to drawing, writing, cutting, and other activities that build up his skills. Eventually he will begin to choose whichever hand works best for each activity.
Also know that you as a right handed person will have some difficulty teaching a left handed child to write so you might want to look up how to do it(this is why many lefties write with their hand turned rather than in the normal writing position).
You might want to buy a pair of left handed scissors as this could be a reason why your son may become uncomfortable and change hands while doing that activity.
Some ideas for a tactile activities that might be fun for him to practice with both hands:
Fill a cookie sheet with sand or shaving cream, then let your children draw in it and smooth it back out (the shaving cream is great for after lunch because you can use it to wash up the table and the hands and it doesn't stain)