Broken record, but tryouts are for the benefit of the club, not the player. They're mostly to fill the lower teams for $$ purposes. When you attend an open tryout you give the power to the Club to assign your kid to a coach and team. Plus, open tryouts are a terrible way to identify a players ability. Don't do it. Instead identify teams and coaches you would want your child to play for. The vast majority of coaches are open to having a new kid practice with a team. Don't know any coaches or teams, ask around. Parents are more than willing to give their opinion.
Contact the coach(s) way ahead of tryouts to join a practice(s). The coach will get a good idea regarding your players abilities, and you will get a good idea of whether the coach and team are a good fit for your kid. Some clubs require existing players to tryout, but otherwise, I would avoid tryouts all together (other than for may be for the youngest new players). They are the worst way to get on a team.
Just be prepared if word gets around to your current coach and club that your practicing with another team. There are couple clubs I know that will expel you immediately if they find out, but that is typically only an issue for the top level teams. Most coaches just get irritated, which is ironic since they wouldn't hesitate to bring a new kid to replace your kid.