The stat buffs are a result of the size changes, so if you got the GM to let you ignore the size increase, they then wouldn't get any benefits.
You do have the option to not take the listed increase at 4th/7th.
Each animal companion has different starting sizes, speed, attacks, ability scores, and special qualities. All animal attacks are made using the creature's full base attack bonus unless otherwise noted. Animal attacks add the animal's Strength modifier to the damage roll, unless it is its only attack, in which case it adds 1-1/2 its Strength modifier. Some have special abilities, such as scent. See Special Abilities for more information on these abilities. As you gain levels, your animal companion improves as well, usually at 4th or 7th level, in addition to the standard bonuses noted on Table: Animal Companion Base Statistics. Instead of taking the listed benefit at 4th or 7th level, you can instead choose to increase the companion's Dexterity and Constitution by 2.
Ok, correction:
If you don't take the size increase, you get a crappy consolation-prize benefit. ;)
Loosing the stats is bad, whats worse is loosing the specials like pounce.