What happens if I go to the US on the first week my visa expires?

If your visa is valid, you can use it to enter the US.

If the visa is valid for the 6 months you noted, then your traveling in April is not when it expires. If the visa is expired, you cannot use it for entry to the US.

If your visa is valid for the time you expect to travel, what should happen is that you would be admitted to the US under the terms of the visa issued to you. A CR-1 is a visa issued to you as the spouse of a US citizen to permit your admission as a conditional resident based on your marriage of less than two years to the US citizen who sponsored you. The visas are generally valid for an extended period of time under the supposition that the visa holder may require time to travel and to make arrangements once a visa is issued. So seems to me that all should be just fine if you travel here to the US during the validity period of the visa you will employ to travel to the US.

As long as your visa is unexpired, DHS should process your immigrant status. You really need to get into the US before the date listed on your visa.