I suspect the Walkman will not provide enough power to drive those headphones properly, but you will only know by trying it. I don't own the headphones, so I don't know for sure. The only heaphones I have used with my Walman are:
1) the included in-ear
2) the Sony MDR-NWN33S
3) the Sony MDR-NWNC200
4) the Sony MDR-7520
#4 requires the most power out of all the above, but they are only 24 ohm headphones. They require very little power to drive, and I get very good sound and loudness at 50% volume using these.
Your 38 ohm headphones will need more power.