I'm a newbie with feline diabetes, and cannot comment on feline asthma at all, so I am NOT giving you cat advice here. However, in case it gives you any ideas for what to ask the vet, I can comment a bit on human asthma plus diabetes (type 1 for me, so completely dependent on insulin). Albuterol has had no noticeable effects on my blood sugar, and neither have either of my maintenance medications. My inhaled maintenance med contains fluticasone propionate (a steroid) and salmeterol (a long-acting bronchodilator), while my maintenance pill contains montelukast sodium, which is a leukotriene receptor antagonist (non-steroidal). All of these have potential side effects, but the one I have had the most issue with is a muscle tremor, mainly only noticeable during fine motor tasks, and minimized at my current dosages.
What did have a huge effect was when I had to temporarily take an oral steroid for my asthma. I ended up having to increase my insulin quite a bit, and my blood sugar went absolutely wild for those few days. But it needed to be done.