Assuming you are in England and Wales you need at least two witnesses.
OK, so what you have suggested will potentially work. But if you get something even very minor wrong it can cost more to sort out in the long run. Even the wording of a survivorship clause (ie if he dies within 6 weeks of me) can cause problems. Some words have very technical meanings which if used incorrectly can result in unfortunate results - eg "all my personal property" would pass a leasehold but not a freehold.
What happens if one of your children dies? Does their share go to their children or to the survivor? What happens if both your children predecease you?
You don't have to appoint an executor, but if you do their authority speaks from death. If you don't appoint an executor the authority can only be conferred by the Probate Registry on application for the grant of letters of administration. This means that until probate has been granted, there is a real limit to what anyone can do.
Why not appoint your spouse or children as executors in the alternative? That way they can deal with things straight away.
I suggest you talk to your solicitor and explain your concerns. You can make a very simple will but it should be well thought out to deal with certain eventualities.