Most universal remotes are only capable of sending the IR signals that they are pre-programmed to send. If you need to create a button that is not pre-programmed, you'll need a remote made by UEI [typically sold under the "One For All" (OFA) brand name] as these remotes usually include a feature called "key mover" that lets you program additional buttons using "advanced codes" (also known as EFCs).

If you were able to find a setup code in your Axim remote, I would expect that most OFA remotes would also have a code for it, but I can't guarantee that. If you were to get an OFA remote and you were able to find a setup code to work your TV, that might give us all the info we need to tell you what code to use to clear the screen, assuming that one of the pre-programmed buttons - like EXIT - doesn't do it already.

If you want to be extra safe, you should get an OFA remote with learning and a JP1 cable, then you could learn the buttons from the Axim remote and decode them using JP1. This would only be necessary if the OFA remote doesn't have a built in code to work the TV.

I would recommend the OFA URC-8820 remote as this has the most Emerson TV codes installed. The Emerson TV codes in this remote are:

0154, 0236, 0463, 0180, 0178, 0171, 0623, 0038, 1911, 1944,
0179, 0019, 1909, 1929, 0185, 0282, 1905, 0039, 1928, 0177, 0280

The only additional Emerson TV codes that I know of are:
0158, 0181, 0182, 0183, 0270

If you like, I could pre-load those codes into a URC-8820 remote for you. I have the URC-8820 available for $19, plus $5 shipping. If you also want a JP1.x cable for this remote, they are $20.