No. I don't think you should and I think that they were misguided in asking you to do so. Naturally, they want the best professional guidance they can get and it is nice to know that they value your opinion so highly.
Nevertheless, you are not the right person. No matter how dispassionate you may think you are, you have formed a vision of "your" school as you wish to see it and you would not be human if that view did not colour your judgment about who you would wish to see carrying on the good work.
It may be that something approaching a clone of you is what the school needs, but it may be that a new style and a new approach might be more appropriate t meet the challenges that lie ahead.
There is nothing to stop you helping the governors, if you really want to do so, but my advice is to thank them for their kindness in asking, suggest where they might go for the help they need and promise your full support in hosting and briefing candidates for the job when they come for interview.
As for the sources of help, the LEA is an obvious one, but, if there is a lack of confidence in them, there are a number of consultancies about, which offer this specific service and a good one is well worth the cost, if you set it against the importance of getting the right person appointed.
Send your queries to Archimedes, The TES, Admiral House, 66-68 East Smithfield, London E1W 1BX or email them to email@example.com.Archimedes cannot enter into any personal correspondence.