回复：我该换成H4呢，还是冒一下险（在线等）

I agree with the 中国律师's suggestion. I do not think "out of status" for one month will be a problem. Actually, you are still lawfully present if your I-94 is still valid. So, just do the H-1 transfer if you get the new job. If your H1 petition is approved without I-94, you just go out of U.S. to get an H1 visa to activate your H1 status.

If you do not get a job after one month, just change your status to H4 or go out of US to get an H4 visa.