Four weeks isnt so long in the big scheme of things. Neither Phyllis nor Kathleen will be going anywhere.
By all means put research to one side for a bit and come back to it - but if you order the Will before you do that, then by the time you come back to it the 4 weeks will have flown by and you will have the Will.
Otherwise when you come back to it, the situation will be just the same, you will be no nearer knowing the answer, and even more time will have passed.
Family History research is not an instant thing (says one who has been at it for about 30 years, and still finds new leads sometimes on something that has been dormant for years), sometimes it is worth waiting to get the vital piece of evidence to move us on. SOmetimes that means waiting for an ordered document to arrive (as in your case) or sometimes it means waiting till one is free to go and visit a Record Office (that might be months) but unless we wait, then we never do the things at all, and then we never make progress!
Sorry, going all profound.
PS Do they accept Postal orders?