Without more information it is hard to answer this. I actually have more questions than answers because not each site is created equally unless they are all brand new:
are they all brand new?
PA/DA equal?
Do any of them have juice?
In general linkbuilding for one way links back to yours with your intent of gaining more juice, linking one site to the next and so-on doesn't do anything for you. If you have a front runner in any of those sites that has good metrics, you can use that site to push juice to others.
What you describe isn't actually a link wheel (it's also black hat tactics), its just one site linking from one to the next without any gain really if they are all equal footing and authority.
A link wheel is like "X" number of edu/gov sites to one site, "X" number of web 2.0 to same site, "X" number of social links etc to same site. White Hat is earning all of it on the merit of your product and/or services and relationships you build. Black Hat is you controlling all of those signals and originating all that juice. Hope that helps.