Yes, that is the way to go, there is an extensive document on disk management and upgrading on the synology knowledgebase that guides you through the process. The operation is not risk free, so have your backups completed in case a disk fails during the stressy 3 times rebuild.
Indeed, you have to go to disk management, deactivate the first HDD, then you pull it out, replace it with your new 6TB (that you, obviously, have surface checked before or made a long smart test) then you repair your volume, once that done, you do it all over again for the 3 other disks.
After that, you have to expand your volume (assuming you only have one) to the new maximum avaible size and voilà.
I just did it on a raid5 made of 9 disks from 6TB to 8TB the disk, took me easily a good big two weeks.
Of course it is best not to use your NAS during that kind of upgrade, at least not heavily. (Anyways, it will be very very slow)
What you can perhaps do, I never tried, is to upgrade one disk, see if you can expand your SHR volume, wait a week, and do it again, and so forth and so on.
This can perhaps help the stress on the 3TB disks wich I think are very quite old.
Also a good idea, is to dismantle your syno, and give it good compressor cleaning, so that you avoid hotspots when you repair the parity.
If your in hot place you can also put fan over the nas, but don't put in the fridge