Can I claim less than my RRSP contribution?

Yes, that is perfectly allowable.
You still need to report all the contributions. On the RRSP/PRPP page, you can tick check the box "Tick the box if you want to claim a less-than-allowable deduction" and put a number into the next box. 0 or empty means no deduction. Then next year, your unused contributions will appear in the box "Amount B - Unused RRSP from previous years".