The file size is right, I don’t think it will be a problem. Even if the patch is not applied correctly, your computer will not be damaged, so please feel free to try it.
I also write about other methods to determine the presence or absence of the header.
The simplest way to determine the presence of the header is to look at the rom extension. Since *.smc files are defined as having headers and *.sfc files are defined as having no headers, a *.smc file will have a header. However, this is a generalization, it depends on how the rom extractor you are using handles filenames, so it is not sure.
If you use TUSH, which I linked to at the top of this topic, it will display dialogue “headered” or “unheadered” after reading the rom. You can then add or remove a header as needed.
Similarly, the website I mentioned has a header detection feature, but it probably only looks at the file size, so it doesn’t have any more information than what you see in the properties.
Advice on patching:
Since SNES emulators automatically apply an ips file with the same name located in the same folder as the loaded rom, the easiest way is to handle the vanilla rom and the ips patch this way. I recommend this method because it does not cause problems like overwriting the vanilla rom by mistake, and it is easy to replace the patch even if the patch is updated frequently.