One should know:  

Just and only for convenience of the interested reader :

cf: Poster Presentation:

by: Kelly SM1, Stepner N1, Marcelo J1, Harrison R1,Yang J1, Yang WH1, Karsh J1 1 Red Maple Trials, Ottawa, Canada 

Presented June 13th, 2016 in Vienna, Austria @ European  Academy of Allergy and Clinical Immunology Annual Meeting

[to be found at:  http://www.redmapletrials.com/wp-content/uploads/RMT-Poster-EAACI2016-CatDander-Vienna-20160613.pdf ]

and:

248       Is There a Time-Dependent Association Between Cat Dander Sampling Time and Feld 1 Levels? by: Jennifer Marcelo, Rachel Harrison, Suzanne M. Kelly, PhD, Ammr Al-Houssan, Nate Stepner, Jimmy Yang, Jacob Karsh, William H. Yang, MD, FAAAAI.    2017 Ann. Meeting American Academy of Allergy, Asthma & Immunology Atlanta, March 3-6,2017. The respective abstract can be found  @ https://aaaai.confex.com/aaaai/2017/webprogram/Paper30581.html.

[see also: http://annualmeeting.aaaai.org/] 

Regarding < 'ideas' welcome >:  I don't have any possibility to evaluate cat (or -generally - pet) dander on filters by and staining  with several acidic or basic dye solutions.  I guess that it might be possible to stain skin dander generally with diluted (i. e. 0.05%) or more concentrated (e.g.0.1 to 0.2%) basic dyes (like Toluidine Blue O or Methylenblue (either as hydrous solution, or eventually also in 70% Ethanol. one should try also either basic or acidified solutions). NB: I have seen (fresh) single human skin cells ("danders") on object slides [mounted with semithin (1µm thickness) resin sections]  due to unclean  treatment or handling of the slide(s) prior to staining als using an 1% - 60% alcoholic solution of basic fuchsin (sometimes with a discernible cell nucleus yet). There might be differences in staining (intensity, specificity) with respect to vitality of the dander (?not quite sure about there existing a plural word "danders"?): dead = totally dried out or somehow vital  / freshly 'harvested' ...

Addendum:  it might be interesting to read also:  "Qualitative Assay of Indoor Air Using an Air Oasis Air Purifier with Special Reference to the Reduction of Aero Allergens and Pollutants"  by GHOSH et al, unfortunately no year of publication given.[only: Report on Phase I: Fall 2006]

some keywords-subtitles : Air Oasis Air Purifier:  plates (petri dishes); Qualitative Assay of the Fungal Aero Allergens (Molds) after using an Air Oasis air purifier; cat and dog dander; Phae III: We will also cover the study on dust mites, insect droppings, other insect residues and animal dander.  

For slide preparation we use standard microscope slides 75x25. Procedure for the preparation of microscopic slides;

Microscopic analysis of collected allergens;

stains: at least  in viewing pollen, including their cell walls and colpi (pores): Safranin O [50:50 mixture of 95% ethanol and distilled water]....

cf:   https://www.hktshop.com/pub/media/wysiwyg/Product_details/Microbereport.pdf

Also you might have a short reading in: 

Canine Pruritus Diagnostics: A Clinical Approach, by ROSENKRANTZ W, PROCEEDINGS: NAVC Conference 2015

Subsection: Hair Coat Collections: "Combing the coat and collecting dander scale and hair...."

Subsection Cytology: ".....easiest stain to use is a commercial modified Wright’s stain like Diff-Quik. This is a Romanovsky-type stain that gives less nuclear detail than a vital stain such as New Methylene blue (NMB)..."

http://www.vetfolio.com/dermatology/canine-pruritus-diagnostics-a-clinical-approach

Best wishes and good luck !

Hi Wolfgang:  Thank you for your responses.  You have referenced some of my earlier work. I am glad that someone follows our work. I am trying to look at this question again with different stains.  I did try the Diff Quik Wright stain, but was not overly impressed with the results. As you know, looking at nuclear material is not really needed, Just trying to find a simple rapid staining that will allow us to easily identify dander.   Many thanks my friend. 

Dear NM Stepner,you're welcome. Would be interetsing to know about your finding a new method/dye recipe for the task (I have not found additional - recent - articles about staining dander - so it is demand for such...), best wishes, good luck and regards, WM.