Pleased to see another Aiwa-lover here, Love Aiwa Walkmans, hate their 2V rechargeables! I tried to find a substitute but gave up.
I do now have some 3.7v LiPo cells, and am looking in to the driving voltages, and charging circuits. The first challenge, however, is getting the faults cleared on the walkmans. I hope to move to the batteries in mid February.
I would not recommend you go down this route. There's a guy in Ebay that builds Aiwa cells that can be recharged with USB if you really want that. I would just find the external AAA battery pack. Based on your electronics experience, building one yourself is a recipe for disaster. Not just for your Aiwa, but as a fire hazard- LiPos are very dangerous! This is a terrible idea.
If you really have no choice, you can find 2 Nimh (2x 1.4v) cells that fit, and modify the battery terminals to route to the external pack inputs. I believe some members have tried this.
I believe the guy on Ebay (I've found him) is actually using LiPo's in the construction anyway. I have invested in some explosion proof bags for the batteries, and I've taken some advice on the batteries and chargers I intend to use. I believe that given the capacities I'm dealing with, that I'm relatively safe. The batteries have both charge and discharge protection circuits.
The problem is sourcing the external AAA battery packs. They are far more rare than the cassette decks themselves. I do have one... but I know they are fragile, and they are also required to power by AC adaptor, as the adaptor goes through the pack to power the unit.
I'm going to repeat this one more time: Don't mess with Lipos! If you reaaaaally want to build a battery pack yourself, go Nimh.
http://www.stereo2go.com/topic/problem-with-aiwas-pb-s5-gumstick-battery---replacement-solution.htm The pictures and links are long dead, but with this information, you should be able to source a 34mm Nimh pack.
I've gone ahead and looked online for batteries for you. I found the half height NiMH gumsticks from the old Aiwa thread. https://www.ebay.com/itm/2-pcs-3-5-...392455?hash=item5440dbb147:g:TaQAAOSwEzxYZNij https://www.ebay.com/itm/1-x-400mah...660687&hash=item237e249690:g:G2IAAOxyOa9R27ux They should fit within the space of the Aiwa battery, if the 3.3mm length is accurate. It will also be much safer than Lipos, and can be charged in any gumstick Nimh charger with extension. 2 of them will add up to 2.4V.