It's possible to mark a virtual disk as "independent-persistent" to exclude it from snapshots.
However, in order to do this you need to first consolidate/delete all the existing snapshots, which can't be done due to the low free disk space, and the thin provisioned virtual disks.
Do you have another disk/LUN to which the current virtual disks can be cloned (manually from the command line)?
Other than this you can backup/restore the VM (requires appropriate licensing, and a backup application), or export the VM to OVF/OVA, and import it again. Both options (backup/restore, and export/import) will consolidate the snapshots. However, these two options require that you delete the VM from disk between the backup/export, and the restore/import, so make sure that you select a reliable target.
In any case, downtime will be required.
Btw. what's the purpose of all the snapshots? Please remember that snapshots are no backups. If the disk/datastore goes south, you may loose everything.
André