The first step in playing in other keys without a capo is knowing the chords used in those keys and where to find them. This is also useful when using a capo too. If someone threw a song at you in a key in which you were not used to playing and if you understood the chords in that key, you could play along even if you only played rhythm and simple rolls and licks over the chords. I recommend starting with this and moving on to learn to play melodies effectively out of different chord shapes like the C and D chords in those keys.
Next, I’m going to provide you with a chart that shows the major and minor chords in several common keys. There will be a quick and basic music theory lesson here but nothing you shouldn’t pick right up on. Try strumming each chord, then using a right-hand vamping pattern, and then using basic rolls of your choice.