I would say it's impossible to do so without first acknowledging that the historic grounding in and modern implementation of pagan spirituality is real. The next step would be identifying how both Hinduism (or spiritual Indian wisdom or whatever moniker you give it) and Christianity see the intrinsic relation between the spiritual and physical realms. If someone is able to paint at least a general picture of the differences, I would start asking what the purpose of trying to separate them would be. Personally I fail to see any advantages in continuing to dwell in a Dorothy-house removed clean away from it's foundations and now situated on someone else's land.
Before I rant on this, let me start by giving a little ground here. I do think that is possible to have physical exercises perhaps physically modelled after those of some other religions ritual without it necessarily making us participants in a false religion. However several objections remain. Certainly not all situations are equal and I have limited experience in the matter, mostly dating to quite a few years ago and discussions I had with folks who were involved. These included some who embraced the conjunction of spiritual and physical exercise, and some who could care less what religion it came from as long as it left them with better digestion.
Now for my rants.
First of all let us address the often forwarded notion of being able to retain the religious elements, but merely in name not in fact. This seems preposterous to me, sort of like trying to use the gutter language of crime to speak of things fair and beautiful. Without the right diction you are stuck in a little box of your own making. Speaking of boxes, it's also like taking the engine out of a car because it ran on the wrong kind of fuel. Without putting another engine in, it make a really useless vehicle, although I suppose it would be good exercise.*
Secondly, the idea that the religious connection can be lost altogether doesn't sit well with me. My initial objection in the first paragraph was that this discussion does not get past square one until we have come to some agreement about there being a connection. The first things I would bring into the discussion is the historical connection, but I think we then need to continue into a discussion about what modern spirituality is like and what kind of world view thinks there is no connection between the spiritual and physical.
I do not think false religions should have all the best exercises any more than I think we should let them have all the best music. However I don't think our best option is to start a bunch of "christian" bands flooding the market with half baked goods but rather to bring back a theological understanding that we are artistic and creative because we are ourselves made in the image of an artistic and creative God. Those who produce anything good or beautiful do so only use a grace given them on loan and it is our job to point out the source and through an understanding and acknowledgement of that grace turn it into worship.
I think something similar ought to be done for exercise. Instead of trying to separate the physical from the spiritual at all, I think it would behove us to develop a biblical understanding of how these things actually relate, then modeling our exercise lives around this. While the things we do with our bodies might resemble Yoga or Tai Chi, it should be carefully delineated what we believe about our bodies being temples of the Spirit so that it is entirely clear to the world what makes us different than them. It seems to be that this is best done at the instructor level and that an individual participating under an instructor with a different world view who is not actively identifying his spiritual beliefs to himself and those he interacts with runs a great risk of not only muddling his own spiritual life but misleading others.
Our sensibilities and sensitivities ought to lead us to actions and words distinct enough that no-one, whether from Hindu, humanistic, christian or undecided world view, could mistake our participation for tacit acceptance of either the premises of a false religion or the decoupling of physical and spiritual realms.
Sometimes it is suggested that such ritual meditations pre-date Christianity and as such might be able to be considered separately from it rather than in competition with it. I think there is a fallacy here in that Christianity did not begin 2k years ago with Jesus or Paul or John the baptist or anyone else, it began with Christ before he created man. And, since the first Adam, Christianity has always looked forward to the coming of the Christ. Thus I think it is silly to claim that anything is pre-christian in the sense of time. Certainly there are sources and influences so we be careful to consider whether the things we include in our lives and practice of Christianity conforms to the Word. I think some pagan rights are actually perversions of things that originated with us. For example ceremonial washings in Islam do not originate there but are actually adaptions of Mosaic law.
*Forgive the pun.