I wouldn't use a correction collar when you are gone.
If he is barking because he is happy to see you, then you don't have a large problem. Some dogs are barky, barking and howling three times when one will do. Consider the breed of your dog. When you come home, will he stop barking when you speak to him? If he is otherwise well behaved and you don't think there are dominance problems, then try teaching him "speak" and "hush". You use treats to reward speak. Once he's trained, tell him speak, then "hush". When you say "hush", you put a chewy treat to his nose. He has to stop barking to sniff. Let him sniff the treat for a couple of seconds, "good dog", then give it to him. Work with him until he can stop barking for ten seconds before giving him a treat. If he is clicker trained, use the clicker.
When he's solid on this you can take it on the road. Bring him to every room of the house playing the speak/hush game, and especially in his crate. Put him in the crate, go outside for a few minutes and come back in. Presumably, he will bark. You tell him "Rover, hush". Then rush to his crate to treat and praise. Repeat several times, making him wait just one second longer. He knows a treat is on it's way for the "hush" trick.
When you come home, he barks, you tell him to hush, hang up your coat and go to the crate to praise and treat. You are training him to acknowledge your presence then shut up.