To answer your question: no, you cannot do it at home. Some analytical techniques are mentioned in the comments.
However I decided to post because LIKELY people should not worry about the Potassium content of table salt.
Table salt (normally "just" NaCl) containing as much of 28.5 % of Potassium (might be more perhaps, but this is what I have at hand) can be sold free of medical prescription not only in drugstores/pharmacies but also in supermarkets, where it can be found in the special diets section or alongside standard salt.
It is a dietary salt indicated to limit the Sodium intake (for instance in case of high blood pressure).
Its price is much higher that that of common salt. It can be used to replace salt in all kitchen uses. It is less salty and more bitter than the normal salt, and one has to "get the mouth" to it.
I would therefore infer that is highly unlikely that something sold as table salt NaCl could contain so much potassium to worry about. Especially when some of those worrying of it, might be prone to buy Potassium integrators during summer :)
Disclaimer: it is clear that the potassium content of whatever table salt sold in food stores and supermarkets should not be matter of concerns however, as for any diets and integrators (Fe, K, Mg...) there exists health conditions which are incompatible. Before starting a diet or taking dietetic salts one should seek the advice of his/her physician.