Is there a risk of increased shedding when stopping spironolactone? if yes, how to best stop to avoid that?

For 40 % of women with androgenetic alopecia, stopping spironolactone will make hair worse.  This is based on Rodney Sinclair’s work showing that about 40 % of women with AGA don’t experience a benefit from spironolactone but the drug helps keep thing where it is. Many treatments for AGA do not grow hair but help stop it. So - absolutely there is a chance you will lose hair by stopping. There is absolutely a chance your hair will say “hey, where is my spironolactone?... bring it back” It’s not a guarantee but these are the facts.

Stopping the spironolactone will not make the hair loss worse, however, you may experience a ‘shedding’ effect after the medication is stopped. This will solely be from the hair follicles releasing old hair, not from new healthy hair releasing. This will be temporary and Nutrafol supplements may help. If it continues, PRP (platelet rich plasma) treatments will help thicken your hair. 
Best,
Dr. Tomar

You may or may not notice any difference in your hair in stopping the Spironolactone however, you may notice changes in your skin as you mention that you have had improvement in your skin.  It may be helpful to seek other treatments for the hair issue while continuing the spironolactone.  Platelet rich plasma, steroid injections, Biotin, Viviscal, Nutrafol or light therapy may help.  Sometimes supplements and other medications that help hair can aggravate acne and skin problems.  Some people notice worsening acne when taking Biotin, or Viviscal for instance.  
Best of luck to you.