I am in a similar situation. Every now and then I use teamviewer for my parents computer.
As teamviewer has a static download link to the last release, it't easy to have a script updating teamvier:
#!/bin/bash
clear
### path for teamviever is ~/programs/ in this case.
### you can change this path to whatever suits you
mkdir cd ~/programs/
sleep 1
cd ~/programs/
rm -R ~/programs/teamviewer
## this will delete ~/programs/teamviewer
## so make sure you do not have by chance a directory ~/programs/teamviewer
## that contains important data
archiv=https://download.teamviewer.com/download/linux/teamviewer_amd64.tar.xz
wget $archiv
tar -xf teamviewer*.tar.xz
rm teamviewer*.tar.xz
notify-send 'TeamViewer Update complete'
exit
This script makes ~/programs/
directory if non-existant, enters directory, deletes current teamviewer directory, downlaods up-to-date teamviever and unpacks it.
You can run teamviewer by clicking on teamviewer in ~/programs/teamviewer
or by running ~/programs/teamviewer/teamviewer
In ~/programs/teamviewer you find a desktop file. You can copy it to ~/.local/share/applications to run teamviewer via start menu.
You can also make a desktop file for the script to run the update via start menu or make a script that updates every time when you run teamviewer or after login.
You need wget installed for the script to work. Can't remember if Solus uses wget or wget 2 currently.