Inner tubes - Thoughts?

Hey, I've been lurking this amazing forum for the past year and been getting out and dirty in my jimmy. Unfortunely, this leads me to my first question for you guys!

Last weekend whilst out on Salisbury I managed to damage the sidewall on one of my tyres. I've spoken to my local tyre fitters expecting them to say it needs replacing but was surprised to find they suggested fitting an inner tube to the current tyre and run is. It's currently on Avon rangers which I understand are tubeless and not designed for this. A quick google has confirmed that this may not be safe, however my tyre fitters are insisting it would be.

To add a spanner to the mix, the current tyres are nearing the end of their life anyway, so really I would like to change for a whole set of new tyres. However, I'm gutted to say we will probably selling the Jimny over the upcoming months as finding we need something bigger for camping and the longer trip we have planned, so really can't justify the £400 for new tyres, especially with a full set of road tyres for it sat in the shed. I'm debating about just sticking them on, but not sure how we will find them Greenlaning in the winter as a bit new to the whole off-road game.

What are your guys thoughts?

In the past I personally have run tubeless maked tyres with inner tubes and never had any issues. Currently my Land Rover has tubes fitted on tubeless rims with remoulds, again no issues and they have been on 10 years at least.
However the reason for tubes in my case was not to correct any visable damage to the tyre. They had tubes fitted as they had a slow puncture or poor seal to the rim. In the case of the Land Rover my past experience of remoulds going flat just made me have tubes fitted from new.
If your sidewall is physically damaged it may not be a good idea.
I am sure the tyre fitter has assessed the damage and feels it is safe, but unfortunately the final call to do so is going to yours to make.