Adapting an older schematic for use with recent components: How might this circuit need to change?
I looked at one of the datasheets for the55 timer. It will operate on 4.5V. That is good.

R8 and R9 will probably need to change so the reset pin keeps the same voltage range. The existing combination seems strange to me as the max would be (9V - 0.2V) * (3.3k / (3.3k + 47k)) or about 0.577 volts. R8 should probably be 0 ohms

Where do you find the specification for 0.3 to 1V on the reset pin?

The voltage change shouldn't affect the 38 khz frequency that the 555 timer generates.