Jon,

The way I clear (Google) searches in Safari 4.0.3, is to use the Clear History in the History Menu Bar.

Is the issue that this technique does not work for you, or that you want to clear recent (Google) searches, but do not wish to lose your history?

Harv
27" i7 iMac (10.13.6), iPhone Xs Max (12.1)

Those who can make you believe absurdities can make you commit atrocities. ~Voltaire