What I'd do:
Month 1: Low intensity cardio (HR 120-140 BPM) on off days. Start with 30 minutes each day, and add 5 minutes per week. By wk 4 you'll be doing 45 minutes of low intensity work 2-3x per week.
Month 2: Drop low intensity work to 2 times per week for 30 minutes. Add alactic sprint work 2x per week after lifting. 6-8 seconds of explosive work, 52-54 seconds of rest. Hill sprints, prowler sprints, etc work well. Follow this progression: wk 1: 6 sprints, wk2-3: 8 sprints, wk 4: 10 sprints.
Month 3: you have some options here. Switch from alactic work to glycolytic stuff (something like a 30:90 work:rest intervals), add a third day of alactic sprints and run the progression again, or just keep on cruising with how things were in Month 2. Make the call based on how you're feeling and if the conditioning is negatively affecting your strength.
That's just one way to set things up, but I like having a plan so it's what I'd do if I were in your shoes. Should be enough work to see some progress in your overall conditioning but not enough to have much of a negative effect on your strength.