Technical difficulties exist. More noticeable the more important the action they are impeding.
On the other hand if they only suffered a minor issue (if any), it could be great to have an excuse to retake an exam they did poorly!
The issue should be approached much earlier than the exam. First of all I would do a full test a few days before. And by full test I mean that it is setup exactly the same way as in the online exam. Even if it's the same platform used for the rest of the course 'with some minor changes', as those might make it no longer work. Or some intervening update might have broken it precisely that day. For example, it would be somewhat riskier than other to plan an important exam the second Wednesday of the month (Microsoft release Windows updates the second Tuesday).
Also, the user may not have been able to test the platform on its own. They may not be able to log in to a room like the one that will be used. The program could crash when talking with other people. It might work for them except when there are many people connected at the same time. They may not be aware that their microphone is not functioning/too low without someone at the other end.
It is also very important to make crystal clear what they should be expecting, e.g. the instructor will be sharing a screen and explaining orally what you must do. You must be viewing their screen, you must hear their instructions, your microphone must work (it will be tested when doing roll call at the beginning) and you shall share your desktop; and what they need to do if any of them fails even in the slightest way, such as calling xxxxxxxxxxx where HelpDesk (or some TA/instructors) will be ready to help them.
Some issues will be simple helpdesk calls (tell the user how to unmute/change volume, describe where button X in the new interface is located), others will depend on external factors such as their connection, and other will be even driver related such as the hardware not being detected properly (no microphone listed, sharing produces a blank screen...) up to completely head-scratching issues.
As an instructor such service serves a double purpose: (a) it helps fixing the minor problems (b) documents the existence of the error. A student that calls you in the first 5 minutes is likely to have a genuine problem. Whereas one that only tells you about that a week later would be met with more suspicion. You will need to actively request errors to be reported, though. You may also want to include it in the exam as 0-point "feedback/suggestions" question (or one showed after finishing). Even if they weren't much affected, you might find things to polish/improve (e.g. setting deadlines of 23:59 rather than 00:00 really improve usability, with almost zero effort. But you need to realize the problem caused by the software showing / users noticing only the day it must be turned in).
Plus, it actually provides a better service and helps the students be more confident in that the technology won't ruin their exam. Then, with more data you will be able to make a better decision. Or even accommodate for the issue on-the-fly (such as having the user joined by phone).
What you definitely don't want is to discover when the exam is about to finish that several students were unable to view the instructor screen [where needed data was provided] during the exam, as they were joining via web interface -the screen only showing on the native app- since the app wasn't opening the room for them!
Even when having two identical installs, on identical hardware, you may find one user is unable to perform an action (such as sharing the screen) which works perfectly for the other. Computers are that funny.
PS: You suggest "allowing to re-take a new exam but have students share their screens" but (a) I don't think that will really avoid someone determined to cheat and (b) if it does help keeping people honest for the exams you do, that should already be happening in the original exam. Another interesting possibility would be to allow an optional re-take for everyone.