So _cat/shards tells you the status, but not how long it needs. It seem to take for ever to initialize a shard.
Have you tried using
_cat/recovery? There isn't an ETA per se, but there are percentages that give you a good idea regarding the completion of shard initialization.
_cat/recovery didn't seem to show data for initializing shards. It's all down so i'll check next time I guess.