This was actually responded to via private e-mail, but since the topic is here as well, I’ll copy that response more or less verbatim.
Yes, AxCrypt is perfectly suited for this scenario. However, the sharing feature does require Premium – at least for the part doing the sharing. I.e., Premium is required to share with someone, but the sharee does not need Premium. In the case you describe, it sounds like your managers would be best served by having Premium, the 2 of them.
Since you’re always getting 30 days free Premium, I suggest you download and try it out. What you are looking for then is the ‘Key Share’ feature, this is what let’s you share the internal file encryption keys with others without sharing your own password.