A generalized Skyrme model of the nucleon supplemented by possible extra terms in the Skyrme Lagrangian is applied to the study of the two-nucleon system. A variational approach taking account of modification of the chiral profile is employed. An adiabatic N-N potential is calculated by the standard spin-isospin projection technique. Several different approaches and parameter choices are examined and compared with each other. No medium-range attraction is found. Modification of some nucleon properties in the interacting system is investigated.