Unfortunately, you cannot currently send individual calls to voicemail on an iPhone without using a non-native app.
From the Skype for Business desktop app (if you are running Click-2-Run build C2R 8201.1002 or later), select Set Up Voice Mail. Change your Call Answering Rules You can change what options your callers have when they reach the voicemail service; get disconnected, hear your greeting, record a message, choose to be transferred to the number or user you select. Change your prompt language This is the prompt language that is played to callers. For list of supported languages, see Languages for voicemail greetings and messages from Skype for Business. Configure your Out of Office greeting This is the customized greeting message that is played to callers when your status is Out of Office. This option can be activated "Always," when you have an active "Auto Reply" in Outlook, or whenever you have an out-of-office calendar appointment.  Where you can get your voicemail messages from

But now I'm going to go ahead and record. So press record sorry I missed your call. Please leave your voicemail after the beep and I'll call you back. Thank you. Press stop and now. I could press play and then if I don't like what I hear, I could press record one more time and when I'm satisfied, I could press save on the top right and it's going to save my greeting and that's all I have to do to set a new voicemail on my iPhone. You could always come back to this page. Press record one more time and replace your voicemail here. You're greeting here, and you should always use someone else's phone to call to see how it sounds from a different device.
If you have voicemails saved on a non-smart phone, your best bet is to record them on a computer. This is a method that requires some equipment, but not as much as you might think.