you don't need an SD-card if you don't need to store samples or want to save/load tables.
There are a few drumsamples loaded into the flash of axoloti (used with the wave/playflash modules) , which you could change with your own samples, still without the need of the SD-card.
But inside the main patch, you can use "embedded" patches, so you could insert your drum patches each in their own embedded patch and assign them each a different midi channel (main patch shares the same channel, although by adjusting the midi module, you can make it so it listen to the channel of your choice). Quite possible I made a module with which you can set your channel manually (sss/midi/...).
So to make an embedded patch:
-insert the module: patch/patcher
-go into that patch-module (edit) and copy your drumpatch in it.
-go to "view" and set the midi-settings (ps. first click on the background to deselect the currently selected module, or you'll get to view the settings of that selected module). Here you can also choose to allow channelselection on the module itself and/or make it polyphonic
-right-click on the controls you want to be able to view on the module and select "parameter on parent"
-go back to your main patch and click "update" on the module