Yes there are restrictions....but first and foremost he should listen to his body, if his symptoms worsen after an activity he should avoid it.
A list of activities to avoid with Chiari and Syringomyelia is posted in the Health Pages....
http://www.medhelp.org/health_pages/list?cid=186
Some with Chiari also have additional related issues where the heat may cause more concern and symptoms to worsen....once all testing is done to see what he has in addition u will know better what he should or should not do.
Use the link I posted to go to the Health Pages to locate the list of activities to avoid and there are other pages of helpful info there too.
To get u started, no straining, lifting, pushing, pulling, bending, roller coasters and things that will bounce him around......