They wouldn't just use a local anesthetic for that surgery, would they?
Wouldn't they need to use a general anesthetic?
この場合、次のような言い方ができますよ。
ーThey wouldn't just use a local anesthetic for that surgery, would they?
「その手術に局所麻酔は使わないでしょ?」
a local anesthetic で「局所麻酔」
ーWouldn't they need to use a general anesthetic?
「全身麻酔使わないといけないんじゃないの?」
a general anesthetic で「全身麻酔」と言えます。
ご参考まで!