You cannot exclude only a single Item but there are ways to manage persistence so that these are not saved. It’s probably a whole lot less work than the path you are heading down. One approach includes: Design Pattern: Group Based Persistence
Note, if you are using rrd4j images are not supported so not saved anyway.
The openHAB cloud server only acts as a proxy to OH. It can only access web pages and files that are hosted by OH itself. It will not give you acces to any files or any other services on your LAN.
If you have static images, you can place them in $OH_CONF/html and access them via https://home.myopenhab.org/static/nameoffile.png. But if the file is in some other folder or served by some other service (e.g. has 192.168… in the address) it’s not supported. Essentially, when you are remote, any URL on your UI must be directly accessible from the Internet or it must be something served up by openHAB itself.