Thank you for thinking about me, but I'm fine walking home.
Thanks for asking. That's nice of you, but I can walk home.
この場合、次のように言うと良いでしょう。
ーThank you for thinking about me, but I'm fine walking home.
「お心遣いありがとうございます。でも歩いて帰るので大丈夫です」
ーThanks for asking. That's nice of you, but I can walk home.
「ご親切にありがとうございます。でも歩いて帰れます」
ご参考まで!