Whether you can do it or not? How could I know? I mean, I don't know anything about your system, so I can't tell whether you can take the impact.
Now, you do say "Standard Edition and 24*7 critical environment." I will say that it sounds to me that you are cheapskate. "24*7 critical" has Enterprise Edition all over it, not only for online index rebuilds.
With Standard Edition, you will have to take downtime, at least when you rebuild critical tables.
I would suggest that you first make a test in a backup environment, so that you can see how long time each table takes, and also how much log you produce and how much the log grows.
REORGANIZE may be an alternative. It does not give equally good results as REBUILD, but it is always an online operation.
Also, investigate if you have to do anything at all. With spinning disks, logical fragmentation is a big thing, that is, the pages in a clustered disk do not come in order on the disk. That matters quite little with SSDs. On the other hand, it is never good to have half-full pages, because that this means that you waste precious buffer-pool memory no nothing.