In macOS High Sierra, I do the following to automate the clicking of the Load Remote Content button in Mail.
Using an Automator Service with setting Service receives [no input] in [Mail] and a Run AppleScript action replacing the default code with the following example AppleScript code and setting a keyboard shortcut in System Preferences > Keyboard > Shortcuts > Services of ⇧⌃⌘L this works for me, however in other versions of macOS the example AppleScript code may need to be adjusted to click the target button.
tell application "System Events" to ¬
tell application process "Mail" to ¬
click button "Load Remote Content" of ¬
group 1 of group 1 of scroll area 2 of ¬
splitter group 1 of splitter group 1 of window 1
Note: I had to add Mail to System Preferences > Security & Privacy > Privacy > Accessibility for this to work.
Note: The example AppleScript code is just that and does not contain any error handling as may be appropriate. The onus is upon the user to add any error handling as may be appropriate, needed or wanted.