छत्रपति can also be
the Tadbhava (तद्भव)
form
of क्षत्रपति.
क्ष in
Sanskrit becomes छ in several Prakrits, examples include छत्री or छत्रिय for Sanskrit क्षत्रिय, छत्रबन्धु for क्षत्रबन्धु, छमा for क्षमा, छार for क्षार, et cetera -
one finds all these usages in the 16th century Awadhi of Ramcharitmanas.
In fact, several Hindi sources refer to the emperor as क्षत्रपति शिवाजी, even though
most spell it as छत्रपति. Many Marathi sources give the spelling छत्रपती (with the long
vowel).
क्षत्रपति also means a sovereign king and is found in Vedic literature. It is used once in Vājasaneyi Saṃhitā (10.17, see here), thrice in Taittirīya Brāhmaṇa (1.7.8.5 and 2.5.7.4, see here) and once in Śatapatha Brāhmaṇa (11.4.3, see here).