First, this is data migration to new platform, so you must always plan for downtime; you can only possibly influence length and number of required downtimes. So if "another way" means "no downtime" - no, this is not possible.
As for swing gear - if using 7MTT CBT, yes - migration from 7G is qualified up to 8.2 and 2650 is supported starting with 9.1, so you cannot migrate (using 7MTT) directly. While migration can be done without using 7MTT, estimating whether it is feasible in your particular case far exceeds the scope of forum format. One thing is sure - doing this without 7MTT will irequire more manual work (and so be more error prone).
Hmm ... if your filer is used exclusively for ESXi datastores - you could simply setup new filer as additional datastore and do storage vMotion. This would be completely transparent and without downtime.