One cheap step you can take is to have the vet run a heartworm test right away -- it's pretty unlikely in Canada, but not impossible. I see lots and lots of murmurs in dogs that have heartworm disease, and they correct after treatment. Those dogs all get spayed and neutered, and they come through fine.
In a HW-negative dog, I think I'd want to start with a chest xray, for the reasons Twyla explained.
Your regular vet can do a chest xray to be sure the heart isn't enlarged due to DCM....and, if needed, that image can probably be sent off to a caridiologist for review for another $50-$100. That's the low-cost way of staring this investigation into cause. As Twyla mentioned, the worry here is that enlargement is a sign of DCM, and DCM means congestive heart failure is on the way. DCM dogs have a shortened lifespan, so it's something any prospective adopter would want to know.
I just had major surgery done on one in rescue with a Grade 4 murmur. The surgeon not only wanted bloodwork, but also a chest x-ray prior to surgery. He sent it to a specialist to review to make sure the heart wasn't enlarged. Only after the specialist confirmed it wasn't enlarged did he go forward with the surgery. This was a complex surgery lasting at least an hour, so the dog was going to be under for a while. However, the surgery was done at a specialty clinic with a state-of-the-art surgery suite, very experienced anesthesia staff, a team of boarded vet specialists AND an emergency ICU on-site...so about as safe a surgery experience as one can possibly set up. The dog came through fine.
An uncomplicated spay can be done fast so they're not under for long at all. HOWEVER, I would not take a dog with a serious murmur to a low-cost spay clinic because they tend to not do an IV-cath with fluids during anesthesia. Assuming the heart isn't enlarged and you are cleared to go forward with the surgery, I'd suggest doing this dog's spay at a full-service clinic that uses fluids during anesthesia. That may potentially factor into the discussion you have with your vet (and cost).