Should the Scrum team members demo their own work in the sprint review

As long as the demo leads to good conversation with the stakeholders about the deliverable and how to adjust what is in the Product Backlog to move forward, in my experience it doesn't matter who does the demos.  

Having said that, if you look at the section of the Scrum Guide on the Sprint Review (https://www.scrumguides.org/scrum-guide.html#events-review), it states that the Development Team does it.  But it also states numerous activities for multiple people in the Scrum Team. But there is also a clause in the section on the Scrum Master (https://www.scrumguides.org/scrum-guide.html#team-sm) that states that they should facilitate scrum events as requested or needed.  So, it could be argued that in your case the Scrum Master is "facilitating" the presentation of the work that has been done per request of the Development Team.  

I will say that if I were the Scrum Master of that team, I would be encouraging the Development Team to do the presentation of the work. 

"...that either the developer or the person that tested the work should show it"

Since there are no individuals and the entire Development Team is responsible for doing the work, again as SM, I'd encourage that one individual do the presentation and find a way to rotate that around the team in future reviews.

I'm working with a team that don't like to demo their own individual work.

How do they feel about demonstrating work as and when it is completed during the Sprint?

I'm working with a team that don't like to demo their own individual work. 

Is there a sense of team-ownership of sprint items?  Is the Development Team comfortable with moving items forward despite individual Dev Team member availability?

At the end of the day, the guide is just that, a guide. You should do the review meeting as it suits you best. If the done work is demonstrated, relevant stakeholder feedback is gathered and the PO talks about the release and the timeline, the meeting reached it's goal. 

Having said that, I do think that presenting an increment or a completed story (and getting feedback):

- is a great motivation anyone who contributed to this work

- is also a skill that at least one person in the dev team should have (ideally multiple or all). It might be a little uneasy and people sometimes have stagefright, but with some preparation (dry run) and with a relaxed and understanding atmosphere can work out very well. 

It might not work everywhere (high level stakeholders are in the room) but I saw a lot of different forms - from small round of people - dev Team, PO, Scrum Master in a meeting room in front of a bigger TV, to company wide Sprint Reviews, with soap bubble making unicorn-toys and employees from different countries (continents) taking part sitting around the stage or over a video-call. 

Anyway, in all cases I saw members of the development team taking pride in demonstrating the work, answering questions. This ultimately lead to a better understanding of the product and a higher motivation. 

Personally, I like to have one of the 3 (in order of preference depending on the nature of the work completed): 1) One of the stakeholders is invited to demonstrate the feature with a development team member or the product owner walking them through it, 2) the development team, or 3) the product owner.

I personally don't think it's good practice for the Scrum Master to demonstrate the increment at Sprint Reviews, but I also make it a goal to make it so I do NOT "lead" any of the events, instead having other team members leading and hosting the events, with me serving a facilitator to ask questions and drive conversation.