Do yourself a favor and DO NOT use dead shrimp. It's a smelly mess (really can get vile) and you have no control of how much ammonia is released nor how fast. If you're bent on a fishless cycle go through the trouble of getting "pure" ammonia (that does NOT foam when shaken) from ACE hardware or Dr Tim's on Amazon. BUT.....
Once your tank is cycled for a week or so, you'll have enough bacteria with which to seed your 2.5g. Take some gravel or up to half of your filter media and put it into the new filter. Introduce your fish and carefully monitor your parameters (in both tanks). Your seeded tank/filter will already be marginally cycled. All you're waiting for here is for your bacteria to multiply and for your cycle to mature and become well-established. As always, aeration is important.
Alternatively, if you have the time, you can run both filters in the cycled tank for a couple of weeks. This will establish a colony in the new filter.
I think it's important with a small tank to have plenty of filter foam for the bacteria to colonize. A couple of extra cubic inches placed in the filter or in the flow will encourage a stable cycle, one that won't break-down easily.
Now, with live bacteria available to you, you'll never have to go through that cycling stress again.
Once a week water changes are nice; just remember: a cycled tank is not for the convenience of the keeper, but for the health and safety of the fish. Check your water frequently.