Liaison office of Grand Ayatullah Sayyid Ali Al Sistani (L.M.H.L) in London, Europe, North and South America.
Apparently, as a precautionary measure, even a boy who is mumayyiz has to be circumcised. A boy who is not yet mumayyiz may perform the ṯawāf without being circumcised, although, as a precaution, it would be better if he were.
#301: If a male pilgrim, man or boy, who is mumayyiz but not circumcised, performs the ṯawāf, it is invalid. If he does not repeat the ṯawāf after having been circumcised, it is deemed undone and the following rules apply to him:
#302: If someone is in possession of the means and is in the position to perform the obligatory pilgrimage but is not circumcised, he should have the circumcision done and then perform the pilgrimage in the same year. Otherwise, he has to postpone it till after the circumcision.
If a circumcision is out of question due to acceptable reasons (e.g. fear of bodily damage), the obligation to perform the pilgrimage is still effective. But as a precaution, in addition to personally performing the ṯawāf for both Hajj and ´Umrah, he should appoint a representative to do the ṯawāf on his behalf. Subsequently, he should not perform the prayer following the ṯawāf until his representative has finished the ṯawāf.