Make "move item" a default right click option
Sam, I don't think it's possible without a third party app. As mentioned by @Tetsujin, there is a native shortcut for moving a file Cmd+C and Cmd+Alt+V, but if you don't wish to use shortcuts, you may have to use a third party app.

I guess you could make an Automator Service, but you'd have to access it from the  "Services" submenu thing and I feel it would be more of a hindrance than a real solution. 

3rd party applications that add "Cut" to the context menu:

All of these applications use the same logic as Windows, when it comes to moving files this way, which is to say backwards from how it works in macs: You start with the intent to "Copy" or "Cut" file(s) and then just normally "Paste" to complete the action. Cutting = Moving.

Should be noted that from 10.11. onward XtraFinder and TotalFinder become more difficult to run, as they need to inject code to Finder and SIP is not into that. I believe both support disabling SIP → installing → enabling SIP. I know TotalFinder does.


XtraFinder - Free app.


Adds "Cut" to the context menu.
XtraFinder Preferences &gt; Features &gt; Cut &amp; Paste

TotalFinder - Paid app.


Adds "Cut" to the context menu. It's on by default. 


There's an alternative Finder Preferences &gt; TotalFinder &gt; Menus &gt; Show CutPaste buttons in Context Menus, which turns Cut Copy Paste into buttons all in one line in the context menu.

Though I'd highly advice against it, you can disable the tabs if that is not your thing.
More or less the same as XtraFinder with some differences.

Path Finder - Paid app.


Path Finder Preferences &gt; Features &gt; Contextual Menu.


Commands list on the left contains all possible context menu items, Cut being one of them and the Contextual Menu list on the right contains all the current items in the context menu. You should be aware that these are contextual... Like for example, you won't see "Copy Dropbox Link" in the actual context menu if the file is not in your Dropbox folder.

Finder replacement. The other two apps extend Finder functionality. 
Has a fully customizable context menu.
In general is more customizable than the other two.
Should be noted that many things that irritate people when they first start using Path Finder can be changed from the View &gt; Show View Options. Some of them being "Bold folders" and "Smart Sorting".



All of these application have shortcuts too: 


Cmd+C = Copy
Cmd+X = Cut
Cmd+V = Paste


Path Finder and XtraFinder both have Move to... and Copy to... context menu items as well.