Yes. Zoomblr shows shinesocold's public posts and profile picture with no Tumblr account or login required. It's completely free.
Open shinesocold on Zoomblr and tap the download button on the avatar to save the full 512px image in its original format (JPG, PNG, GIF, or WebP).
Each image in shinesocold's feed has its own download button — tap it to save the picture in full resolution. Photosets give you a button per image.
Zoomblr is a free Tumblr viewer — view and download any public blog's avatar and posts without an account.