I will reiterate my position on pull through type cleaning tools. They are better seen and not used.
The Martini is very easily disassembled. Disassemble it and remove the breech block and use and angular brush to clean the chamber. Make up a muzzle protector and use a proper coated cleaning rod.
Pull throughs are for amateurs IMHO. If used with proper muzzle protectors and proper techniques they are OK but you really need to be properly prepared to use them. Just remember, they aren't making any more barrels for those old girls. You need to treat them accordingly. The metal in those barrels are softer than what is used today so improper use of a pull through cleaner could prove disastrous after several cleanings.
I talked to a old REME that was a close friend before he passed on. One of his biggest peeves was the extensive muzzle wear caused by improperly used pull through cleaning tools in the field. Ask yourself why you see so many Springfields, Mausers, SKSs, Mosins etc with counterbores. Do it right every time and you won't do any irreparable harm to irreplaceable parts.