The difference between a mild and regular accelerator is the main ingredient in it. Most regular accelerators are acetone based, while mild may be heptane or even naphtha based. You have to look at the MSDS to determine what type you are actually getting. With that in mind, the o rings and seals that are in some sprayers will not stand up to acetone, the will become soft and deform or maybe even to the point of dissolving. Keep in mind that it is not the base that actually caused the acceterator to start hardening the CA, it's another ingredient listed on the MSDS usually in an amount of less that 5%.
Which ever refillable sprayer you are considering, you need to call the vendor and discuss your needs.
When I first started using a refillable spray can, I purchased the cheap ones from Harbor Freight for $5-$10 each. After going through about 3 or 4 because they started leaking from use with an acetone based accelerator, I looked for a better sprayer.