Asanas are generally acceptable if you leave the ideological side of it and when you do the Asana be aware of the posture and sensation in the body. For timing purposes use the breath and hear beat. This can be a good physical exercise.
If you leave out the ideological part behind Pranayama then both are compatible. The distinction between the two are:
- Buddhism: do not regulate the breath but watch the process initially but later slow the process
- Pranayama: regulate the process
Some buddhist tradition sometimes do advice to regulate the breath to overcome being scatterbrained when meditating, being lethargic, and to induce pleasantness / joy. Also there is a view that Pranayama could have been originating or evolution from a Buddhist teaching. (See: Can Pranayama Be Derived from Anapana?)
Also when doing Breath Meditation some traditions mention certain prominent places to rest your attention. If you go by the Suttas only it say to rest the attention in front or around the mouth as some traditions interpret. (See Parimukhaṁ). This can be analogous to Chakras in Yoga. (See: Are the Chakras present in the original Buddha's teachings?).
Whatever you do start with at then end you have to see things as they are. For this you have to reduce the of the breath and develop strong awareness. If you are in regulating the process you lose the chance of being objectively observing and being aware. The awareness you develop would be shallow. This might be a hindrance later on. But if this is not the only techniques you use then it can become a tool. In addition you are creating new fabrication / conditioned existence where the objective was to get out of it. Having said that the path leading to the final goal is actually fabricated / conditioned. Sometimes good conditioning can help.
Having said all this do not give too much prominence of time to Yoga though it can be used for benefit as time is limited but use this as a tool in certain situation like to overcome lethargy, develop energy, overcome pain, etc.
For an alternate discussion see: Yoga: as seen in the light of Vipassana