There’s no reason to not do HIIT, with a little bit of work you can manage your diabetes alongside your training. I train 6 days a week at a minimum, all heavy weight sessions with 20/30 minute HIIT cardio. HIIT or steady state cardio can improve insulin sensitivity. Going for a walk fair enough is still exercise but personally for me it just wouldn’t cut it for a good ‘workout’.
With good control & a little understanding you can easily control your levels. I’ll always have a prework meal which on a low carb day would be a banana with 25g of peanut butter it would also be the same for a medium carb day. For a high carb day I would have a blueberry muffin, one of the big ones you get in the packs of 4. I’ll then train & afterwards have a post workout protein shake as well as Rice Krispies cereal. Low day would be 40Grams of cereal, medium day would be 60grams then finally high carb day would be 100Grams of cereal. Might seem like a huge amount especially when 100Grams of Rice Krispies contains 82 grams of carbs but if you’ve got your ratios right you’ll be absolutely fine.
One thing I would say is don’t do any sort of training if you’ve had a hypo within 24hrs of your session especially if your kinda new to the gym. You’ll be more prone to having another hypo.