There are two methods of changing what pet you have equipped while playing a pet minigame.
Jammer wall method
This method only lets you switch pets once while playing.
Step 1: Go up to the pet minigame and then quickly open your jammer wall, click the game icon, click the photo booth in the top left, and then click "change your animal". It is easier to do when you're lagging a bit.
Step 2: You can go into your pet menu and unequip or change your pet. Then, exit and you can play the game.Desync method
Step 1: Desync once
Step 2: Go to your spare's den, then the place where the pet minigame is. Make sure you have the right pet equipped.
Step 3: Play the pet minigame and then switch your spare's den to an underwater one.
Step 4: You are now playing the pet mini-game as either an underwater pet or no pet, depending on what your underwater animal has equipped. You can also switch your spare's den back to a land den and you will be playing as your land animal's pet again. You can't switch your land animal's pet with this method however.
Semi-Player Game Method
Step 1: Host a semi-player game in your alt's den.
Step 2: Go to the land with the pet game. Line up the "join me" button of the game so it's at the side of your alt's screen. Then, drag your spare's window over so the button is next to the pet game button.
Step 3: Click on join me, then the pet game button immediately after. Then exit the semi-player game on both accounts. Your main account will be at your spare's den.
Step 4: If your spare changes the den to underwater, you will now be playing the pet game as whatever pet your ocean animal has equipped. You can also switch your spare's den back to a land den and you will be playing as your land animal's pet again. You can't switch your land animal's pet with this method however.
Effects
In Sssssnake, you can get the same golden mouse over and over if you don't have a pet equipped. The first time you eat a golden mouse, it will disappear but you can go over the same spot where it was to get it multiple times. This can cause you to get an absurd amount of golden mice. Unfortunately if you get too many mice it doesnt give you the gems for it :(
It does however, give you the achievement for "5 golden mice in one game".
This glitch perhaps has one of the biggest downsides. If you collect over 100 golden mice without a pet equipped, your trading will get disabled (AJC only) after you reload. I remember i had to contact AJ to get it fixed D:
The other two pet minigames play normally when played without a pet equipped, although i think the disabled trading glitch will apply to those two if you went through the effort of getting 100 golden discs or duckys.
Playing any pet minigame as the wrong animal doesn't have an effect either. If the pet you're playing it with can't have an effect, it will probably glitch your trading if you gather 100 of the golden items.
You can even do the jammer wall method while desynced to do both at the same time if you wanted to switch from snake to another pet to no pet. Switching back to a land den will cause you to play with the pet you switched to on your land animal.
If you're glitched the wrong animal by the switch animals glitch, the pet of the animal you actually are will be used in the pet game.