This one's particularly dangerous
Sorry to be a killjoy, but modifying this unit is not a good idea unless you like risking fire and shock. In theory, such a mod could work, but the unit is already dangerous.
I've got a couple of these LED chains with flasher control units off eBay, and they're all unsafe. Similar ones have been banned in the EU and recalled, mainly because they are a fire and electric shock hazard. Definitely don't leave them unattended, and keep children, pets, and anything flammable (e.g. your house) away from them.
The wires attached to the contacts have too small a cross-section (0.11mm²) for carrying mains (the two contacts at the left of the pic above) or a measured 208V DC, which is the maximum output on each of the 4 lines (the one on the extreme right of the picture is the common line). The same type of wire is used for both mains and DC feeds.
The wire also has no resistance to being stretched and broken, so you can end up with live wires pulled out of the flasher if a child or pet treads on the mains lead. Cable strain relief is provided by glueing the wires into the flasher control box, but one gentle pull broke the mains wire outside the box, and left live strands easily accessible.
I replaced the mains lead with proper 2-core mains flex for safety, so I could test it. The feeds to the led chains (25 LEDs per chain) are PWM - the power is rapidly switched off and on, being left on for a longer period when the LEDs need to appear at their brightest. Bypassing the switching PCR406s will only add to the risk of shock, so I'd recommend chucking the flasher unit into a dustbin. Keep the LEDs for another project (with a lower voltage feed - not mains).
You would be better off going to a reputable high-street seller, paying a few quid extra, and getting a non-flashing set of lights which you can use for several years without injuring anyone or starting a fire.
Hope this helps.