There is no one in the office that can act as my sub, I don't have anyone above me other than the board.
Is the issue that you don’t know what to explain to people... or rather that an appropriate back up plan for handling issues while you are gone isn’t in place? Those are two different things.
I understand that only the board is above you. Unless your job duties absolutely require contact on vacation, then you don’t have anything to explain about why you are gone. It’s vacation. I get that your staff wants you to be accessible while on vacation, and maybe even you are struggling with letting go enough to not be in contact during the vacation. If your job requires contact while on vacation and you need to justify that to HR or the board, then I’d consider getting a doctor’s letter to verify that you have “a health matter” to address that requires not being responsible for job duties while on vacation for the very select few people that need to know and approve it as an ADA covered change in the policy regarding required contact on vacation. Then figure out the best possible plan for handling all matters while you are gone.
But if this is more of a matter that you feel pressure or indirect responsibility to explain because others are going to be taking on tasks that they are not used to talking on, or delaying things until you get back because there isn’t a sub filling your shoes and etc, or you otherwise feel pressure to justify/explain the vacation, that’s not really going to be resolved by going into details about why you are gone or making up an excuse. It’s not really everyone’s business why you are gone.
I have a business mentor who is retired but was in a very high position with many who depended on him. He also didn’t have a boss except his board and regulatory offices. We have talked a lot about how to explain the absences I have to the from work at times. He has talked a lot about how he and staffers would explain absences - sometimes even 6 month long absences - very briefly and vaguely. Ninety nine percent of the time, they wouldn’t explain why even the CEO was gone to anyone but maybe 1 trusted friend in the company. One top staffer was even getting cancer care and wasn’t likely to live (but did), another doing a rehab for an addiction, etc.
This stuff happens a lot more than most people think it does. People have stuff they have to deal with that requires time off and not being reachable. It happens.
None of them bothered with explaining to all their staff and certainly not the board why they were gone. Any explanation would have been debated, gossiped, and not helpful to staff. It might make the person who is gone feel better for a brief time, but it actually didn’t help anyone else. The staff only knew they were in a sabbatical or a vacation and not reachable until they returned. The end.
This is an extreme example, with details changed to keep the situation private. But something much like this happened: One time, a key top level staffer in his organization was on a month long sabbatical (which was actually 30 days in rehab for a drug addiction) when someone on staff was kidnapped and decisions had to be made that normally were made by that one person. The state dept was involved and everything. All the staff knew was that the key staffer could not be reached. Knowing more about why that person couldn’t be reached didn’t help them deal with the absence.
Same for more common situations like the copy machine breaks down... knowing why you can’t be reached to handle it doesn’t help then handle it.
I strongly suggest focus more on giving your staff the tools to cover things for a few weeks until you are gone than explaining why you are gone. It will help them more to be vague about the reasons for the absence... but be specific about how to handle things while gone.
If you want to get into why you are gone because of the depth of the relationships you have built, then I would pick one person to tell more details, but pick someone you would trust to keep it confidential. If that person doesn’t exist in the workplace, then just don’t go there. Focus on why people are asking more about why you will be gone: 1.) they care about you and want to know you better (and you can talk about other things) 2.) they are nervous about doing their job while you are gone. As s leader in the organization, focus especially on number 2 and the vacation as a whole will go over better than if you give extensive excuses for it.