I am not sure what's happening with CDFPlayer. There is nothing on http://www.wolfram.com/cdf-player/ to indicate that a V10 compatible version is on its way...

Perhaps someone from WRI could comment?

An option that you may have for your clients and students is a cloud deployment of your CDFs. I don't know what the issues might be though in terms of credits as well as different functionality on the cloud vs having a Mathematica Kernel and FrontEnd running on your local CPU...

UndoTrackedVariables is an option associated with the new Undo/Redo functionality in version 10. When you execute a Manipulate command, the resulting internals of the Cell that displays the Manipulate has in it the UndoTrackedVariables option. This is what the version 9 CDFPlayer is generating an error mesage for,

For example, the following Manipulate

Manipulate[x, {x, 1, 2}]

has as its output cell expression

Cell[BoxData[
   TagBox[
     StyleBox[
       DynamicModuleBox[{$CellContext`x$$ = 1, Typeset`show$$ = True, 
      Typeset`bookmarkList$$ = {}, 
          Typeset`bookmarkMode$$ = "Menu", Typeset`animator$$, 
      Typeset`animvar$$ = 1, Typeset`name$$ = 
           "\"untitled\"", Typeset`specs$$ = {{
               Hold[$CellContext`x$$], 1, 2}}, 
      Typeset`size$$ = {8., {0., 9.}}, Typeset`update$$ = 0, 
          Typeset`initDone$$, 
      Typeset`skipInitDone$$ = True, $CellContext`x$2065$$ = 0}, 
         DynamicBox[Manipulate`ManipulateBoxes[
            1, StandardForm, "Variables" :> {$CellContext`x$$ = 1}, 
       "ControllerVariables" :> {
                 Hold[$CellContext`x$$, $CellContext`x$2065$$, 0]}, 
             "OtherVariables" :> {
                Typeset`show$$, Typeset`bookmarkList$$, 
         Typeset`bookmarkMode$$, Typeset`animator$$, 
                 Typeset`animvar$$, Typeset`name$$, Typeset`specs$$, 
         Typeset`size$$, Typeset`update$$, 
                 Typeset`initDone$$, Typeset`skipInitDone$$}, 
       "Body" :> $CellContext`x$$, 
             "Specifications" :> {{$CellContext`x$$, 1, 2}}, 
       "Options" :> {}, "DefaultOptions" :> {}],
           ImageSizeCache -> {247., {49., 54.}},
           SingleEvaluation -> True],
         Deinitialization :> None,
         DynamicModuleValues :> {},
         SynchronousInitialization -> True,
         UndoTrackedVariables :> {Typeset`show$$, 
       Typeset`bookmarkMode$$},
         UnsavedVariables :> {Typeset`initDone$$},
         UntrackedVariables :> {Typeset`size$$}], "Manipulate",
       Deployed -> True,
       StripOnInput -> False],
     Manipulate`InterpretManipulate[1]]], "Output"]

This beeping is normally displayed when we are dealing with different versions, and it does not means that there is something wrong, but it is just a warning about that some functionality can be missed. However, the fact that there is not CDF Player for Mathematica 10 implies that even the best approach to solve the problem will have to deal with this beeping.

Nevertheless, I agree with you, for readers it immediately throws a cloud of doubt over the entire document. But it is out of our will, it is an issue for Wolfram's guys!

The following worked for me:

1) Export your CDF/nb as Standalone: File -> CDF Export -> Standalone

2) Open the standalone CDF with any text editor (I used Notepad++) and automatically replace all the instructions: "UndoTrackedVariables:>{Typesetshow$$, TypesetbookmarkMode$$}," (without quotation marks, but including the comma at the end) by empty-space. That is, simply delete them and save the document.

3) Open the CDF with Mathematica 10. You will see the beeping: "The file you are opening appears to have been edited outside of the Wolfram System. The file outline cache was ignored. This should not affect any of the contents of the file." . That's okay, just click OK and next save the CDF Standalone as CDF: File-> Save as (*.cdf)

4) Next, the cdf can be open with CDF Player 9. You will see the beeping: "This notebook was created in a more recent version of Mathematica, and may not function properly with the older front end you are using. Contact Wolfram Research (www.wolfram.com) for upgrade information." But that's okay too, the CDF normally work without any problem with normal environment, at least for me.

Hope this could help

My first try was really to use this script. Unfortunately, it doesn't worked for me and still I don't know why. So, I had to look for alternatives. Basically, I did manually what it is supposed that this script must do.