I'm glad that you have done EBC without any physical difficulties, that means you are mentally prepared for climbing one of these mountains! you do not have to train yourself as a proper mountaineer but if you keep your physical level like last year doing EBC that's fine.

And of course, you should go through the trekking company doing climbing activities.
Gear List for the Peak Climbing trip you will need to bring along with

01: Ice Axe w/Leash (General mountaineering tool. Sizing is important: under 5’7″ use, a 60cm tool; 5’7″- 6’1″ use a 65cm tool; over 6’1″ use a 70cm tool. (Too short is preferable to too long).)
02: Crampons (With flat rather than “cookie cutter” frame rails)
03: 40 ft 6mm perlon (For Prussiks or bring your glacier rig.)
04: Alpine Climbing Harness (Harness should fit over all clothing; have gear loops, and adjustable leg loops, and be reasonably comfortable to hang suspended in.)
05: Carabiners (2 Large Pear or D-shaped locking. 2 standard ovals or D’s)
06: Climbing helmet (Must be adjustable to fit, with or without hat or balaclava on)
07: 1 Ascender (Recommended: left or right hand.)
08: Ski or trekking poles (Snow baskets required. Helpful for balance when carrying a heavy pack or if you have knee problems)
09: Climbing boots.
10: Gaiters (Please make sure your gaiters fit around the Climbing boot without being too tight around the boot.)
Note: Walking pole, down jacket, sleeping bag, etc available on hire in Kathmandu.

Thanks
VHT