The HTTP headers always apply to only one item. In the case of those set on the page itself they apply only to the page and not to the linked resources.
Browsers and HTTP caches in the wild will have cached copies of this image already. There is no way to force them to reload the image without changing the URL of the image (which you've stated you cannot do).
If this is the only time you are changing this image, or you expect such changes to be infrequent, then just change the image and eventually the web will cache the new image. Browsers that check for updated versions will be notified by the web server that the timestamp has changed.
For making a more permanent change, you need to investigate how IIS is setting headers for your static files. I suspect that it sets all the headers uniformly for all files, but there may be a way to override the headers for a specific file. If not, you should be able to wrap the request for that url in a script which sets the headers before delivering the content. What you want to do, in this case, is set the Expires or max-age header so that browsers know how long they should keep this item in the cache. Note that these headers will only apply to future requests for this file.
Putting these headers in the pages themselves will not affect requests for the file. Be careful when adding cache-control headers as your site may not function properly if the wrong things are being cached too aggressively; alternatively your bandwidth may spike as things are not being cached which should be.
For future consideration you should make it possible to change the paths of static resources when the content changes. This makes it clear to a browser that the file is new because there will be nothing with that url in the path. For example:
www.yoursite.com/images/v1/logo.png
becomes
www.yoursite.com/images/v2/logo.png
once logo.png changes to v2. Then, in the pages where logo.png is referenced, you have code to automatically write the correct url in the page. This way each revision of the file has a unique name and thus never conflicts with any previously cached versions.