Apple Watch Charger from 2019 (Apple Watch 4 Series)

I looked at prior responses but just want to make sure. I just purchased a new Apple Watch 9 Series because the ECG heath app was dying so to speak. A new charging cable was enclosed with the watch but not a new adapter like I got with my Apple 14 Pro last year. That adapter was much larger than prior phones. The new cable comes with a smaller connection so it will not fit in the older adapter. Is it safe to use the old charger and older adapter or would it be best to buy a newer adapter that may be more powerful? Thanks