Is impedance matching a requirement for CAT-5e traces?
About trace length matching:

IEEE 802.3 specifies propagation delay and not distance (see 23.6.2.4 Delay from IEEE standard section 2).
It says that you should have a maximum propagation delay of 570ns for your entire link and also propagation speed per meter should not exceed 5.7ns/m (thus the 100 meter common "limit").

But you are not concerned by these specs (just a reminder, in case you have a long link).


  23.6.2.4.3 Difference in link delays
  The difference in propagation delay, or skew, under all conditions, between the fastest and the slowest simplex
  link segment in a link segment shall not exceed 50 ns at all frequencies between 2.0 MHz and
  12.5 MHz. It is a further functional requirement that, once installed, the skew between all pair combinations
  due to environmental conditions shall not vary more than ± 10 ns, within the above requirement.


You should retain that the maximum skew allowed on your whole link is around 10% of the maximum propagation delay (570 ns). As you are designing a custom adapter, we will take large margins to simplify computations and consider your adapter is equivalent to 1 meter of link.

So the maximum propagation delay allowed for your segment is 1/100 of 570ns = 5.7ns.
The allowed skew between pairs is 1/100 of 50 ns = 500 ps.

Given your routing specs, the propagation delay of the signal is around 50 ps/cm.
So with a 500 ps allowed skew delay, you can have a length difference of 10 cm.

No worries here.

Also, about EM leakage, 100 Mbits Ethernet signal frequency is 12.5 MHz, even if it is rise time equivalent frequency that matters, you don't have to worry to much if you are following advices given here by Dzarda and dextorb