How do I choose a cable /cord, connected to mains part, that is compliant with IEC 60601-1 3rd ed.?
I can't speak for medical but to pass regulatory you need to make sure each part of the AC mains system has a certification. The power supply has to have the IEC60601-1 Certification (XP power has some good medical grade supplies with medical certifications.) The line filter\fuse box will need to be certified. Any of your own harnessing will need to follow creepage and clearance distances AND have a sufficient wire size and insulation. Your application may require isolation, so then your power supply will have to be isolated and you will have to incorporate this into you design.
Usually with the IEC standard they will tell you one thing and it applies to another section, they are really difficult to read and even the regulatory companies don't know all of the standard. (I had a regulatory tester try and certify an industrial product under a residential testing process, we had to convince them that ours was industrial)
The goal is to pass regulatory, they will check your design. You will probably want to start working with them now, they might charge you to answer questions, but it's better to change your design now than have it fail regulatory. Find some help for your specific type of device either from a consultant or somebody who has been through the process before. Either that or buy all of the certification documents (they are expensive, and can be a few hundred a piece.) then read them 10x through. Usually you need to make sure all the components you buy have the appropriate certifications.
Edit: I was looking through a power supply guide for an unrelated reason and I found this  (Power Supply
Technical Guide 2010/11).
From page 84:

Currently the standard is available in both 2nd edition and 3rd edition. The 2nd edition is IEC60601-
1:2003 and 3rd edition is IEC60601-1:2005. The 3rd edition was published in 2005 after 10 years of
development. Its purpose is to harmonize the terminology contained in the 2nd edition with other
standards such as IEC60950.
The 3rd edition differs from the 2nd edition putting emphasis on the OEM implementing a risk management system compliant with ISO14971. It also introduces new concepts such as essential performance of equipment and distinguishes between the operator and the patient with MOOP
(Means Of Operator Protection) and MOPP (Means of Patient Protection).
The concept of MOPP and MOOP allows the manufacturer relaxation in terms of creepage &amp; clearance distances for MOOP if it is proven through risk management that the equipment will not come into contact with the patient in normal operation or under a single fault condition. The requirements for MOOP follow IEC60950 and for MOPP follow those required in IEC60601-1 2nd edition.
The structure of the base standard is hazard specific and provides requirements for evaluating the common hazards associated with electro-medical products. Its scope is to protect both patients and operators by reducing the likelihood of electric shock, mechanical, radiation, ignition of flammable anaesthetics, fire and excessive output energy hazards. The basic concept of the standard requires that two means of protection (MOP) or two levels of protection (LOP) under IEC60601-1 2nd edition are employed in various areas of the product so that
if one fails the product will retain another means of protection to contain any electrical shock hazard from either the patient or the operator.
To achieve these two means of protection, 60601-1 permits the use of three building blocks used in different combinations. These building blocks are insulation, protective earth and protection impedance. For example protective earth (1 x MOP) used in conjunction with basic insulation (1 x
MOP) provides the two means of protection required. The table below lists the permitted building blocks and the means of protection they provide.
Before the design can start the insulation class of the equipment must be determined; whether the equipment will be class I (reliant on protective earth) or class II (not reliant on protective earth) as must the classification of the applied part if applicable.